CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-sticky-header-enabled vector-toc-available" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>Wormhole - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-sticky-header-enabled vector-toc-available";var cookie=document.cookie.match(/(?:^|; )enwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy", "wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgRequestId":"aefb6b98-ad5d-43d9-8215-f6f1627d0f21","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Wormhole","wgTitle":"Wormhole","wgCurRevisionId":1276143628,"wgRevisionId":1276143628,"wgArticleId":34043,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["CS1 maint: location missing publisher","Articles with short description","Short description matches Wikidata","All articles with unsourced statements","Articles with unsourced statements from August 2023","Articles with unsourced statements from February 2025","Wikipedia articles needing clarification from March 2017","Wikipedia articles needing page number citations from January 2018","Commons category link is on Wikidata","Webarchive template wayback links","Wormhole theory","Albert Einstein", "Astronomical hypotheses","Black holes","Conjectures","Exotic matter","Faster-than-light travel","General relativity","Gravity","Hypothetical astronomical objects","Lorentzian manifolds","Space","Theory of relativity","Time travel"],"wgPageViewLanguage":"en","wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Wormhole","wgRelevantArticleId":34043,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":false,"wgFlaggedRevsParams":{"tags":{"status":{"levels":1}}},"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"en","pageLanguageDir":"ltr","pageVariantFallbacks":"en"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":false,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":60000,"wgEditSubmitButtonLabelPublish":true, "wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q7544","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.math.styles":"ready","ext.cite.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","jquery.makeCollapsible.styles":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready", "ext.wikimediaBadges":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","mediawiki.page.media","ext.scribunto.logs","site","mediawiki.page.ready","jquery.makeCollapsible","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.ReferenceTooltips","ext.gadget.switcher","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=en&modules=ext.cite.styles%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cjquery.makeCollapsible.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=en&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=en&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.16"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Einstein-rosen-bridge-model.png/1200px-Einstein-rosen-bridge-model.png"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="786"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Einstein-rosen-bridge-model.png/800px-Einstein-rosen-bridge-model.png"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="524"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Einstein-rosen-bridge-model.png/640px-Einstein-rosen-bridge-model.png"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="419"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Wormhole - Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//en.m.wikipedia.org/wiki/Wormhole"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=Wormhole&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (en)"> <link rel="EditURI" type="application/rsd+xml" href="//en.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://en.wikipedia.org/wiki/Wormhole"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom feed" href="/w/index.php?title=Special:RecentChanges&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Wormhole rootpage-Wormhole skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Jump to content</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" title="Main menu" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Main menu" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Main menu</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Main menu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">hide</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigation </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z"><span>Main page</span></a></li><li id="n-contents" class="mw-list-item"><a href="/wiki/Wikipedia:Contents" title="Guides to browsing Wikipedia"><span>Contents</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:Current_events" title="Articles related to current events"><span>Current events</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:Random" title="Visit a randomly selected article [x]" accesskey="x"><span>Random article</span></a></li><li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:About" title="Learn about Wikipedia and how it works"><span>About Wikipedia</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us" title="How to contact Wikipedia"><span>Contact us</span></a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> Contribute </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:Contents" title="Guidance on how to use and edit Wikipedia"><span>Help</span></a></li><li id="n-introduction" class="mw-list-item"><a href="/wiki/Help:Introduction" title="Learn how to edit Wikipedia"><span>Learn to edit</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Community_portal" title="The hub for editors"><span>Community portal</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:RecentChanges" title="A list of recent changes to Wikipedia [r]" accesskey="r"><span>Recent changes</span></a></li><li id="n-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_upload_wizard" title="Add images or other media for use on Wikipedia"><span>Upload file</span></a></li><li id="n-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages"><span>Special pages</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Main_Page" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="The Free Encyclopedia" src="/static/images/mobile/copyright/wikipedia-tagline-en.svg" width="117" height="13" style="width: 7.3125em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Special:Search" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Search Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia" aria-label="Search Wikipedia" autocapitalize="sentences" title="Search Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personal tools"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Appearance" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Appearance</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en" class=""><span>Donate</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:CreateAccount&returnto=Wormhole" title="You are encouraged to create an account and log in; however, it is not mandatory" class=""><span>Create account</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:UserLogin&returnto=Wormhole" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o" class=""><span>Log in</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Log in and more options" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Personal tools" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Personal tools</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en"><span>Donate</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:CreateAccount&returnto=Wormhole" title="You are encouraged to create an account and log in; however, it is not mandatory"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Create account</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:UserLogin&returnto=Wormhole" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Log in</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pages for logged out editors <a href="/wiki/Help:Introduction" aria-label="Learn more about editing"><span>learn more</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:MyContributions" title="A list of edits made from this IP address [y]" accesskey="y"><span>Contributions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:MyTalk" title="Discussion about edits from this IP address [n]" accesskey="n"><span>Talk</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contents" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contents</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Visualization_technique" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Visualization_technique"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Visualization technique</span> </div> </a> <ul id="toc-Visualization_technique-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Terminology" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Terminology"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Terminology</span> </div> </a> <button aria-controls="toc-Terminology-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Terminology subsection</span> </button> <ul id="toc-Terminology-sublist" class="vector-toc-list"> <li id="toc-Modern_definitions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Modern_definitions"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Modern definitions</span> </div> </a> <ul id="toc-Modern_definitions-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Development" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Development"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Development</span> </div> </a> <button aria-controls="toc-Development-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Development subsection</span> </button> <ul id="toc-Development-sublist" class="vector-toc-list"> <li id="toc-Schwarzschild_wormholes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Schwarzschild_wormholes"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Schwarzschild wormholes</span> </div> </a> <ul id="toc-Schwarzschild_wormholes-sublist" class="vector-toc-list"> <li id="toc-Einstein–Rosen_bridges" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Einstein–Rosen_bridges"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.1</span> <span>Einstein–Rosen bridges</span> </div> </a> <ul id="toc-Einstein–Rosen_bridges-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Traversable_wormholes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Traversable_wormholes"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Traversable wormholes</span> </div> </a> <ul id="toc-Traversable_wormholes-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Raychaudhuri's_theorem_and_exotic_matter" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Raychaudhuri's_theorem_and_exotic_matter"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Raychaudhuri's theorem and exotic matter</span> </div> </a> <ul id="toc-Raychaudhuri's_theorem_and_exotic_matter-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Modified_general_relativity" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Modified_general_relativity"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Modified general relativity</span> </div> </a> <ul id="toc-Modified_general_relativity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Faster-than-light_travel" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Faster-than-light_travel"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Faster-than-light travel</span> </div> </a> <ul id="toc-Faster-than-light_travel-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Time_travel" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Time_travel"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Time travel</span> </div> </a> <ul id="toc-Time_travel-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Interuniversal_travel" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Interuniversal_travel"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Interuniversal travel</span> </div> </a> <ul id="toc-Interuniversal_travel-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Metrics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Metrics"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Metrics</span> </div> </a> <ul id="toc-Metrics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_fiction" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#In_fiction"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>In fiction</span> </div> </a> <ul id="toc-In_fiction-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>References</span> </div> </a> <button aria-controls="toc-References-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle References subsection</span> </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Citations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Citations"> <div class="vector-toc-text"> <span class="vector-toc-numb">13.1</span> <span>Citations</span> </div> </a> <ul id="toc-Citations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">13.2</span> <span>Sources</span> </div> </a> <ul id="toc-Sources-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">14</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Wormhole</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 67 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-67" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">67 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Wurmgat" title="Wurmgat – Afrikaans" lang="af" hreflang="af" data-title="Wurmgat" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AB%D9%82%D8%A8_%D8%AF%D9%88%D8%AF%D9%8A" title="ثقب دودي – Arabic" lang="ar" hreflang="ar" data-title="ثقب دودي" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Furacu_de_gux%C3%A1n" title="Furacu de guxán – Asturian" lang="ast" hreflang="ast" data-title="Furacu de guxán" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Soxulcan_d%C9%99liyi" title="Soxulcan dəliyi – Azerbaijani" lang="az" hreflang="az" data-title="Soxulcan dəliyi" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%95%E0%A7%8D%E0%A6%B7%E0%A7%81%E0%A6%A6%E0%A7%8D%E0%A6%B0%E0%A6%AC%E0%A6%BF%E0%A6%AC%E0%A6%B0" title="ক্ষুদ্রবিবর – Bangla" lang="bn" hreflang="bn" data-title="ক্ষুদ্রবিবর" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9A%D1%80%D0%B0%D1%82%D0%BE%D0%B2%D0%B0%D1%8F_%D0%BD%D0%B0%D1%80%D0%B0" title="Кратовая нара – Belarusian" lang="be" hreflang="be" data-title="Кратовая нара" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9A%D1%80%D0%B0%D1%82%D0%BE%D0%B2%D0%B0%D1%8F_%D0%BD%D0%B0%D1%80%D0%B0" title="Кратовая нара – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Кратовая нара" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A7%D0%B5%D1%80%D0%B2%D0%B5%D0%B9%D0%BD%D0%B0_%D0%B4%D1%83%D0%BF%D0%BA%D0%B0" title="Червейна дупка – Bulgarian" lang="bg" hreflang="bg" data-title="Червейна дупка" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Wuamloch" title="Wuamloch – Bavarian" lang="bar" hreflang="bar" data-title="Wuamloch" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Forat_de_cuc" title="Forat de cuc – Catalan" lang="ca" hreflang="ca" data-title="Forat de cuc" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9A%D0%B0%D1%8E%D1%80%D0%B0_%D1%85%C4%83%D0%B2%C4%83%D0%BB%C4%95" title="Каюра хăвăлĕ – Chuvash" lang="cv" hreflang="cv" data-title="Каюра хăвăлĕ" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/%C4%8Cerv%C3%AD_d%C3%ADra" title="Červí díra – Czech" lang="cs" hreflang="cs" data-title="Červí díra" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Ormehul" title="Ormehul – Danish" lang="da" hreflang="da" data-title="Ormehul" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Wurmloch" title="Wurmloch – German" lang="de" hreflang="de" data-title="Wurmloch" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Ussiauk" title="Ussiauk – Estonian" lang="et" hreflang="et" data-title="Ussiauk" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A3%CE%BA%CE%BF%CF%85%CE%BB%CE%B7%CE%BA%CF%8C%CF%84%CF%81%CF%85%CF%80%CE%B1" title="Σκουληκότρυπα – Greek" lang="el" hreflang="el" data-title="Σκουληκότρυπα" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Agujero_de_gusano" title="Agujero de gusano – Spanish" lang="es" hreflang="es" data-title="Agujero de gusano" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Vermotruo" title="Vermotruo – Esperanto" lang="eo" hreflang="eo" data-title="Vermotruo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Zizare_zulo" title="Zizare zulo – Basque" lang="eu" hreflang="eu" data-title="Zizare zulo" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%85%E2%80%8C%DA%86%D8%A7%D9%84%D9%87" title="کرم‌چاله – Persian" lang="fa" hreflang="fa" data-title="کرم‌چاله" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Trou_de_ver" title="Trou de ver – French" lang="fr" hreflang="fr" data-title="Trou de ver" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Wjirmgat" title="Wjirmgat – Western Frisian" lang="fy" hreflang="fy" data-title="Wjirmgat" data-language-autonym="Frysk" data-language-local-name="Western Frisian" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Poll_p%C3%A9iste" title="Poll péiste – Irish" lang="ga" hreflang="ga" data-title="Poll péiste" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Burato_de_verme" title="Burato de verme – Galician" lang="gl" hreflang="gl" data-title="Burato de verme" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9B%9C%ED%99%80" title="웜홀 – Korean" lang="ko" hreflang="ko" data-title="웜홀" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%88%D6%80%D5%A4%D5%B6%D5%A1%D5%AD%D5%B8%D5%BC%D5%B8%D5%B9" title="Որդնախոռոչ – Armenian" lang="hy" hreflang="hy" data-title="Որդնախոռոչ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Crvoto%C4%8Dina" title="Crvotočina – Croatian" lang="hr" hreflang="hr" data-title="Crvotočina" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ig mw-list-item"><a href="https://ig.wikipedia.org/wiki/Oghere_Worm" title="Oghere Worm – Igbo" lang="ig" hreflang="ig" data-title="Oghere Worm" data-language-autonym="Igbo" data-language-local-name="Igbo" class="interlanguage-link-target"><span>Igbo</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Lubang_cacing" title="Lubang cacing – Indonesian" lang="id" hreflang="id" data-title="Lubang cacing" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Ormag%C3%B6ng" title="Ormagöng – Icelandic" lang="is" hreflang="is" data-title="Ormagöng" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%97%D7%95%D7%A8_%D7%AA%D7%95%D7%9C%D7%A2%D7%AA" title="חור תולעת – Hebrew" lang="he" hreflang="he" data-title="חור תולעת" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/L%C3%A8ng_cacing" title="Lèng cacing – Javanese" lang="jv" hreflang="jv" data-title="Lèng cacing" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%AD%E1%83%98%E1%83%98%E1%83%A1_%E1%83%AE%E1%83%95%E1%83%A0%E1%83%94%E1%83%9A%E1%83%98" title="ჭიის ხვრელი – Georgian" lang="ka" hreflang="ka" data-title="ჭიის ხვრელი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Foramen_vermis" title="Foramen vermis – Latin" lang="la" hreflang="la" data-title="Foramen vermis" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/T%C4%81rpeja" title="Tārpeja – Latvian" lang="lv" hreflang="lv" data-title="Tārpeja" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Kirmgrau%C5%BEa" title="Kirmgrauža – Lithuanian" lang="lt" hreflang="lt" data-title="Kirmgrauža" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/F%C3%A9regj%C3%A1rat" title="Féregjárat – Hungarian" lang="hu" hreflang="hu" data-title="Féregjárat" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A6%D1%80%D0%B2%D0%BE%D1%82%D0%BE%D1%87%D0%B8%D0%BD%D0%B0" title="Црвоточина – Macedonian" lang="mk" hreflang="mk" data-title="Црвоточина" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B5%E0%B4%BF%E0%B4%B0%E0%B4%A6%E0%B5%8D%E0%B4%B5%E0%B4%BE%E0%B4%B0%E0%B4%82" title="വിരദ്വാരം – Malayalam" lang="ml" hreflang="ml" data-title="വിരദ്വാരം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Lubang_cecacing" title="Lubang cecacing – Malay" lang="ms" hreflang="ms" data-title="Lubang cecacing" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Wormgat" title="Wormgat – Dutch" lang="nl" hreflang="nl" data-title="Wormgat" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%AF%E3%83%BC%E3%83%A0%E3%83%9B%E3%83%BC%E3%83%AB" title="ワームホール – Japanese" lang="ja" hreflang="ja" data-title="ワームホール" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Ormehull" title="Ormehull – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Ormehull" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Ormeh%C3%B2l" title="Ormehòl – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Ormehòl" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Krot_uyasi" title="Krot uyasi – Uzbek" lang="uz" hreflang="uz" data-title="Krot uyasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Tunel_czasoprzestrzenny" title="Tunel czasoprzestrzenny – Polish" lang="pl" hreflang="pl" data-title="Tunel czasoprzestrzenny" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Buraco_de_minhoca" title="Buraco de minhoca – Portuguese" lang="pt" hreflang="pt" data-title="Buraco de minhoca" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Gaur%C4%83_de_vierme" title="Gaură de vierme – Romanian" lang="ro" hreflang="ro" data-title="Gaură de vierme" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D1%80%D0%BE%D1%82%D0%BE%D0%B2%D0%B0%D1%8F_%D0%BD%D0%BE%D1%80%D0%B0" title="Кротовая нора – Russian" lang="ru" hreflang="ru" data-title="Кротовая нора" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Wormhole" title="Wormhole – Simple English" lang="en-simple" hreflang="en-simple" data-title="Wormhole" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/%C4%8Cervia_diera" title="Červia diera – Slovak" lang="sk" hreflang="sk" data-title="Červia diera" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/%C4%8Crvina" title="Črvina – Slovenian" lang="sl" hreflang="sl" data-title="Črvina" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A6%D1%80%D0%B2%D0%BE%D1%82%D0%BE%D1%87%D0%B8%D0%BD%D0%B0" title="Црвоточина – Serbian" lang="sr" hreflang="sr" data-title="Црвоточина" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Crvoto%C4%8Dina" title="Crvotočina – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Crvotočina" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Madonreik%C3%A4" title="Madonreikä – Finnish" lang="fi" hreflang="fi" data-title="Madonreikä" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Maskh%C3%A5l" title="Maskhål – Swedish" lang="sv" hreflang="sv" data-title="Maskhål" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%85%E0%AE%A3%E0%AF%8D%E0%AE%9F%E0%AE%B5%E0%AF%86%E0%AE%B3%E0%AE%BF_%E0%AE%AA%E0%AF%81%E0%AE%B4%E0%AF%81%E0%AE%A4%E0%AF%8D%E0%AE%A4%E0%AF%81%E0%AE%B3%E0%AF%88" title="அண்டவெளி புழுத்துளை – Tamil" lang="ta" hreflang="ta" data-title="அண்டவெளி புழுத்துளை" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A4%D3%99%D0%B7%D0%B0_%D1%82%D0%B8%D1%88%D0%B5%D0%B3%D0%B5" title="Фәза тишеге – Tatar" lang="tt" hreflang="tt" data-title="Фәза тишеге" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A3%E0%B8%B9%E0%B8%AB%E0%B8%99%E0%B8%AD%E0%B8%99" title="รูหนอน – Thai" lang="th" hreflang="th" data-title="รูหนอน" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%9A%D0%B8%D1%80%D0%BC%D1%87%D0%BE%D0%BB%D0%B0" title="Кирмчола – Tajik" lang="tg" hreflang="tg" data-title="Кирмчола" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Solucan_deli%C4%9Fi" title="Solucan deliği – Turkish" lang="tr" hreflang="tr" data-title="Solucan deliği" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D1%80%D0%BE%D1%82%D0%BE%D0%B2%D0%B8%D0%BD%D0%B0_(%D1%84%D1%96%D0%B7%D0%B8%D0%BA%D0%B0)" title="Кротовина (фізика) – Ukrainian" lang="uk" hreflang="uk" data-title="Кротовина (фізика)" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%88%D8%B1%D9%85_%DB%81%D9%88%D9%84" title="ورم ہول – Urdu" lang="ur" hreflang="ur" data-title="ورم ہول" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/L%E1%BB%97_s%C3%A2u" title="Lỗ sâu – Vietnamese" lang="vi" hreflang="vi" data-title="Lỗ sâu" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E8%99%AB%E6%B4%9E" title="虫洞 – Wu" lang="wuu" hreflang="wuu" data-title="虫洞" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E8%9F%B2%E6%B4%9E" title="蟲洞 – Cantonese" lang="yue" hreflang="yue" data-title="蟲洞" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%99%AB%E6%B4%9E" title="虫洞 – Chinese" lang="zh" hreflang="zh" data-title="虫洞" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q7544#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Wormhole" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:Wormhole" rel="discussion" title="Discuss improvements to the content page [t]" accesskey="t"><span>Talk</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Change language variant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">English</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Views"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Wormhole"><span>Read</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Wormhole&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Wormhole&action=history" title="Past revisions of this page [h]" accesskey="h"><span>View history</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Tools" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Tools</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Tools</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">hide</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Actions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Wormhole"><span>Read</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Wormhole&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Wormhole&action=history"><span>View history</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:WhatLinksHere/Wormhole" title="List of all English Wikipedia pages containing links to this page [j]" accesskey="j"><span>What links here</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:RecentChangesLinked/Wormhole" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k"><span>Related changes</span></a></li><li id="t-upload" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:File_Upload_Wizard" title="Upload files [u]" accesskey="u"><span>Upload file</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Wormhole&oldid=1276143628" title="Permanent link to this revision of this page"><span>Permanent link</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Wormhole&action=info" title="More information about this page"><span>Page information</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:CiteThisPage&page=Wormhole&id=1276143628&wpFormIdentifier=titleform" title="Information on how to cite this page"><span>Cite this page</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FWormhole"><span>Get shortened URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FWormhole"><span>Download QR code</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Print/export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=Wormhole&action=show-download-screen" title="Download this page as a PDF file"><span>Download as PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Wormhole&printable=yes" title="Printable version of this page [p]" accesskey="p"><span>Printable version</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In other projects </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Wormholes" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q7544" title="Structured data on this page hosted by Wikidata [g]" accesskey="g"><span>Wikidata item</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Hypothetical topological feature of spacetime</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For other uses, see <a href="/wiki/Wormhole_(disambiguation)" class="mw-disambig" title="Wormhole (disambiguation)">Wormhole (disambiguation)</a>.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Einstein-rosen-bridge-model.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Einstein-rosen-bridge-model.png/290px-Einstein-rosen-bridge-model.png" decoding="async" width="290" height="190" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Einstein-rosen-bridge-model.png/435px-Einstein-rosen-bridge-model.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Einstein-rosen-bridge-model.png/580px-Einstein-rosen-bridge-model.png 2x" data-file-width="2040" data-file-height="1336" /></a><figcaption>A wormhole visualized as a two-dimensional surface. Route (a) is the shortest path through normal space between points 1 and 2; route (b) is a shorter path through a wormhole.</figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><style data-mw-deduplicate="TemplateStyles:r1246091330">.mw-parser-output .sidebar{width:22em;float:right;clear:right;margin:0.5em 0 1em 1em;background:var(--background-color-neutral-subtle,#f8f9fa);border:1px solid var(--border-color-base,#a2a9b1);padding:0.2em;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse;display:table}body.skin-minerva .mw-parser-output .sidebar{display:table!important;float:right!important;margin:0.5em 0 1em 1em!important}.mw-parser-output .sidebar-subgroup{width:100%;margin:0;border-spacing:0}.mw-parser-output .sidebar-left{float:left;clear:left;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-none{float:none;clear:both;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-outer-title{padding:0 0.4em 0.2em;font-size:125%;line-height:1.2em;font-weight:bold}.mw-parser-output .sidebar-top-image{padding:0.4em}.mw-parser-output .sidebar-top-caption,.mw-parser-output .sidebar-pretitle-with-top-image,.mw-parser-output .sidebar-caption{padding:0.2em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-pretitle{padding:0.4em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-title,.mw-parser-output .sidebar-title-with-pretitle{padding:0.2em 0.8em;font-size:145%;line-height:1.2em}.mw-parser-output .sidebar-title-with-pretitle{padding:0.1em 0.4em}.mw-parser-output .sidebar-image{padding:0.2em 0.4em 0.4em}.mw-parser-output .sidebar-heading{padding:0.1em 0.4em}.mw-parser-output .sidebar-content{padding:0 0.5em 0.4em}.mw-parser-output .sidebar-content-with-subgroup{padding:0.1em 0.4em 0.2em}.mw-parser-output .sidebar-above,.mw-parser-output .sidebar-below{padding:0.3em 0.8em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:115%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist"><tbody><tr><th class="sidebar-title"><a href="/wiki/General_relativity" title="General relativity">General relativity</a></th></tr><tr><td class="sidebar-image"><span class="notpageimage" typeof="mw:File"><a href="/wiki/File:Spacetime_lattice_analogy.svg" class="mw-file-description" title="Spacetime curvature schematic"><img alt="Spacetime curvature schematic" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Spacetime_lattice_analogy.svg/220px-Spacetime_lattice_analogy.svg.png" decoding="async" width="220" height="82" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Spacetime_lattice_analogy.svg/330px-Spacetime_lattice_analogy.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Spacetime_lattice_analogy.svg/440px-Spacetime_lattice_analogy.svg.png 2x" data-file-width="1260" data-file-height="469" /></a></span><div class="sidebar-caption" style="padding:0.5em 0.2em 0.6em;border-bottom:1px solid #aaa; display:block;margin-bottom:0.1em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Λ</mi> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>κ</mi> </mrow> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/124ab80fcb17e2733cc17ff6f93da5e52f355c77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:19.468ex; height:2.843ex;" alt="{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}"></span></div></td></tr><tr><td class="sidebar-content" style="padding-bottom:0.75em;"> <ul><li><a href="/wiki/Introduction_to_general_relativity" title="Introduction to general relativity">Introduction</a></li> <li><div class="hlist"><ul><li><a href="/wiki/History_of_general_relativity" title="History of general relativity">History</a></li><li><a href="/wiki/Timeline_of_gravitational_physics_and_relativity" title="Timeline of gravitational physics and relativity">Timeline</a></li><li><a href="/wiki/Tests_of_general_relativity" title="Tests of general relativity">Tests</a></li></ul></div></li> <li><a href="/wiki/Mathematics_of_general_relativity" title="Mathematics of general relativity">Mathematical formulation</a></li></ul></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;;color: var(--color-base)"><div class="sidebar-list-title-c">Fundamental concepts</div></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Equivalence_principle" title="Equivalence principle">Equivalence principle</a></li> <li><a href="/wiki/Special_relativity" title="Special relativity">Special relativity</a></li> <li><a href="/wiki/World_line" title="World line">World line</a></li> <li><a href="/wiki/Pseudo-Riemannian_manifold" title="Pseudo-Riemannian manifold">Pseudo-Riemannian manifold</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="background:#ddf; text-align:center;;color: var(--color-base)"><div class="sidebar-list-title-c">Phenomena</div></div><div class="sidebar-list-content mw-collapsible-content hlist"><table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base, #202122 ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Two-body_problem_in_general_relativity" title="Two-body problem in general relativity">Kepler problem</a></li> <li><a href="/wiki/Gravitational_lens" title="Gravitational lens">Gravitational lensing</a></li> <li><a href="/wiki/Gravitational_redshift" title="Gravitational redshift">Gravitational redshift</a></li> <li><a href="/wiki/Gravitational_time_dilation" title="Gravitational time dilation">Gravitational time dilation</a></li> <li><a href="/wiki/Gravitational_wave" title="Gravitational wave">Gravitational waves</a></li> <li><a href="/wiki/Frame-dragging" title="Frame-dragging">Frame-dragging</a></li> <li><a href="/wiki/Geodetic_effect" title="Geodetic effect">Geodetic effect</a></li> <li><a href="/wiki/Event_horizon" title="Event horizon">Event horizon</a></li> <li><a href="/wiki/Gravitational_singularity" title="Gravitational singularity">Singularity</a></li> <li><a href="/wiki/Black_hole" title="Black hole">Black hole</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#ececff; font-style:italic;font-weight:normal;"> <a href="/wiki/Spacetime" title="Spacetime">Spacetime</a></th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Spacetime_diagram" title="Spacetime diagram">Spacetime diagrams</a></li> <li><a href="/wiki/Minkowski_space" title="Minkowski space">Minkowski spacetime</a></li> <li><a class="mw-selflink selflink">Einstein–Rosen bridge</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;;color: var(--color-base)"><div class="sidebar-list-title-c"><div class="hlist"><ul><li>Equations</li><li>Formalisms</li></ul></div></div></div><div class="sidebar-list-content mw-collapsible-content hlist"><table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base, #202122 ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none;padding-bottom:0;margin-bottom:0;"><tbody><tr><th class="sidebar-heading" style="font-style:italic;font-weight:normal;padding-bottom:0;"> Equations</th></tr><tr><td class="sidebar-content" style="padding-top:0;"> <ul><li><a href="/wiki/Linearized_gravity" title="Linearized gravity">Linearized gravity</a></li> <li><a href="/wiki/Einstein_field_equations" title="Einstein field equations">Einstein field equations</a></li> <li><a href="/wiki/Friedmann_equations" title="Friedmann equations">Friedmann</a></li> <li><a href="/wiki/Geodesics_in_general_relativity" title="Geodesics in general relativity">Geodesics</a></li> <li><a href="/wiki/Mathisson%E2%80%93Papapetrou%E2%80%93Dixon_equations" title="Mathisson–Papapetrou–Dixon equations">Mathisson–Papapetrou–Dixon</a></li> <li><a href="/wiki/Hamilton%E2%80%93Jacobi%E2%80%93Einstein_equation" title="Hamilton–Jacobi–Einstein equation">Hamilton–Jacobi–Einstein</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;font-weight:normal;padding-bottom:0;"> Formalisms</th></tr><tr><td class="sidebar-content" style="padding-top:0;"> <ul><li><a href="/wiki/ADM_formalism" title="ADM formalism">ADM</a></li> <li><a href="/wiki/BSSN_formalism" title="BSSN formalism">BSSN</a></li> <li><a href="/wiki/Parameterized_post-Newtonian_formalism" title="Parameterized post-Newtonian formalism">Post-Newtonian</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;font-weight:normal;padding-bottom:0;"> Advanced theory</th></tr><tr><td class="sidebar-content" style="padding-top:0;"> <ul><li><a href="/wiki/Kaluza%E2%80%93Klein_theory" title="Kaluza–Klein theory">Kaluza–Klein theory</a></li> <li><a href="/wiki/Quantum_gravity" title="Quantum gravity">Quantum gravity</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;;color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Exact_solutions_in_general_relativity" title="Exact solutions in general relativity">Solutions</a></div></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Schwarzschild_metric" title="Schwarzschild metric">Schwarzschild</a> (<a href="/wiki/Interior_Schwarzschild_metric" title="Interior Schwarzschild metric">interior</a>)</li> <li><a href="/wiki/Reissner%E2%80%93Nordstr%C3%B6m_metric" title="Reissner–Nordström metric">Reissner–Nordström</a></li> <li><a href="/wiki/Einstein%E2%80%93Rosen_metric" title="Einstein–Rosen metric">Einstein–Rosen waves</a></li> <li><a class="mw-selflink selflink">Wormhole</a></li> <li><a href="/wiki/G%C3%B6del_metric" title="Gödel metric">Gödel</a></li> <li><a href="/wiki/Kerr_metric" title="Kerr metric">Kerr</a></li> <li><a href="/wiki/Kerr%E2%80%93Newman_metric" title="Kerr–Newman metric">Kerr–Newman</a></li> <li><a href="/wiki/Kerr%E2%80%93Newman%E2%80%93de%E2%80%93Sitter_metric" title="Kerr–Newman–de–Sitter metric">Kerr–Newman–de Sitter</a></li> <li><a href="/wiki/Kasner_metric" title="Kasner metric">Kasner</a></li> <li><a href="/wiki/Lema%C3%AEtre%E2%80%93Tolman_metric" title="Lemaître–Tolman metric">Lemaître–Tolman</a></li> <li><a href="/wiki/Taub%E2%80%93NUT_space" title="Taub–NUT space">Taub–NUT</a></li> <li><a href="/wiki/Milne_model" title="Milne model">Milne</a></li> <li><a href="/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric" title="Friedmann–Lemaître–Robertson–Walker metric">Robertson–Walker</a></li> <li><a href="/wiki/Oppenheimer%E2%80%93Snyder_model" title="Oppenheimer–Snyder model">Oppenheimer–Snyder</a></li> <li><a href="/wiki/Pp-wave_spacetime" title="Pp-wave spacetime">pp-wave</a></li> <li><a href="/wiki/Van_Stockum_dust" title="Van Stockum dust">van Stockum dust</a></li> <li><a href="/wiki/Weyl%E2%80%93Lewis%E2%80%93Papapetrou_coordinates" title="Weyl–Lewis–Papapetrou coordinates">Weyl−Lewis−Papapetrou</a></li> <li><a href="/wiki/Hartle%E2%80%93Thorne_metric" title="Hartle–Thorne metric">Hartle–Thorne</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;;color: var(--color-base)"><div class="sidebar-list-title-c">Scientists</div></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz</a></li> <li><a href="/wiki/David_Hilbert" title="David Hilbert">Hilbert</a></li> <li><a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Poincaré</a></li> <li><a href="/wiki/Karl_Schwarzschild" title="Karl Schwarzschild">Schwarzschild</a></li> <li><a href="/wiki/Willem_de_Sitter" title="Willem de Sitter">de Sitter</a></li> <li><a href="/wiki/Hans_Reissner" title="Hans Reissner">Reissner</a></li> <li><a href="/wiki/Gunnar_Nordstr%C3%B6m" title="Gunnar Nordström">Nordström</a></li> <li><a href="/wiki/Hermann_Weyl" title="Hermann Weyl">Weyl</a></li> <li><a href="/wiki/Arthur_Eddington" title="Arthur Eddington">Eddington</a></li> <li><a href="/wiki/Alexander_Friedmann" title="Alexander Friedmann">Friedmann</a></li> <li><a href="/wiki/Edward_Arthur_Milne" title="Edward Arthur Milne">Milne</a></li> <li><a href="/wiki/Fritz_Zwicky" title="Fritz Zwicky">Zwicky</a></li> <li><a href="/wiki/Georges_Lema%C3%AEtre" title="Georges Lemaître">Lemaître</a></li> <li><a href="/wiki/J._Robert_Oppenheimer" title="J. Robert Oppenheimer">Oppenheimer</a></li> <li><a href="/wiki/Kurt_G%C3%B6del" title="Kurt Gödel">Gödel</a></li> <li><a href="/wiki/John_Archibald_Wheeler" title="John Archibald Wheeler">Wheeler</a></li> <li><a href="/wiki/Howard_P._Robertson" title="Howard P. Robertson">Robertson</a></li> <li><a href="/wiki/James_M._Bardeen" title="James M. Bardeen">Bardeen</a></li> <li><a href="/wiki/Arthur_Geoffrey_Walker" title="Arthur Geoffrey Walker">Walker</a></li> <li><a href="/wiki/Roy_Kerr" title="Roy Kerr">Kerr</a></li> <li><a href="/wiki/Subrahmanyan_Chandrasekhar" title="Subrahmanyan Chandrasekhar">Chandrasekhar</a></li> <li><a href="/wiki/J%C3%BCrgen_Ehlers" title="Jürgen Ehlers">Ehlers</a></li> <li><a href="/wiki/Roger_Penrose" title="Roger Penrose">Penrose</a></li> <li><a href="/wiki/Stephen_Hawking" title="Stephen Hawking">Hawking</a></li> <li><a href="/wiki/Amal_Kumar_Raychaudhuri" title="Amal Kumar Raychaudhuri">Raychaudhuri</a></li> <li><a href="/wiki/Joseph_Hooton_Taylor_Jr." title="Joseph Hooton Taylor Jr.">Taylor</a></li> <li><a href="/wiki/Russell_Alan_Hulse" title="Russell Alan Hulse">Hulse</a></li> <li><a href="/wiki/Willem_Jacob_van_Stockum" title="Willem Jacob van Stockum">van Stockum</a></li> <li><a href="/wiki/Abraham_H._Taub" title="Abraham H. Taub">Taub</a></li> <li><a href="/wiki/Ezra_T._Newman" title="Ezra T. Newman">Newman</a></li> <li><a href="/wiki/Shing-Tung_Yau" title="Shing-Tung Yau">Yau</a></li> <li><a href="/wiki/Kip_Thorne" title="Kip Thorne">Thorne</a></li> <li><a href="/wiki/List_of_contributors_to_general_relativity" title="List of contributors to general relativity"><i>others</i></a></li></ul></div></div></td> </tr><tr><td class="sidebar-below hlist" style="background-color: transparent; border-color: #A2B8BF"> <ul><li><span class="nowrap"><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/14px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="14" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/21px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/28px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-file-width="530" data-file-height="600" /></a></span> </span><a href="/wiki/Portal:Physics" title="Portal:Physics">Physics portal</a></span></li> <li><span class="nowrap"><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:General_relativity" title="Category:General relativity">Category</a></span></li></ul></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:General_relativity_sidebar" title="Template:General relativity sidebar"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:General_relativity_sidebar" title="Template talk:General relativity sidebar"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:General_relativity_sidebar" title="Special:EditPage/Template:General relativity sidebar"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>A <b>wormhole </b>is a hypothetical structure which connects disparate points in <a href="/wiki/Spacetime" title="Spacetime">spacetime</a>. It may be visualized as a tunnel with two ends at separate points in spacetime (i.e., different locations, different points in time, or both). Wormholes are based on a special <a href="/wiki/Solutions_of_the_Einstein_field_equations" title="Solutions of the Einstein field equations">solution of the Einstein field equations</a>.<sup id="cite_ref-NYT-20221010_1-0" class="reference"><a href="#cite_note-NYT-20221010-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Specifically, they are a transcendental <a href="/wiki/Bijection" title="Bijection">bijection</a> of the spacetime continuum, an <a href="/wiki/Asymptote" title="Asymptote">asymptotic</a> projection of the <a href="/wiki/Calabi%E2%80%93Yau_manifold" title="Calabi–Yau manifold">Calabi–Yau manifold</a> manifesting itself in <a href="/wiki/Anti-de_Sitter_space" title="Anti-de Sitter space">anti-de Sitter space</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Wormholes are consistent with the <a href="/wiki/General_relativity" title="General relativity">general theory of relativity</a>, but whether they actually exist is unknown. Many scientists postulate that wormholes are merely projections of a <a href="/wiki/Four-dimensional_space" title="Four-dimensional space">fourth spatial dimension</a>, analogous to how a two-dimensional (2D) being could experience only part of a three-dimensional (3D) object.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> A well-known analogy of such constructs is provided by the <a href="/wiki/Klein_bottle" title="Klein bottle">Klein bottle</a>, displaying a hole when rendered in three dimensions but not in four or higher dimensions. </p><p>In 1995, <a href="/wiki/Matt_Visser" title="Matt Visser">Matt Visser</a> suggested there may be many wormholes in the universe if <a href="/wiki/Cosmic_string" title="Cosmic string">cosmic strings</a> with <a href="/wiki/Negative_mass" title="Negative mass">negative mass</a> were generated in the <a href="/wiki/Chronology_of_the_universe" title="Chronology of the universe">early universe</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Some physicists, such as <a href="/wiki/Kip_Thorne" title="Kip Thorne">Kip Thorne</a>, have suggested how to make wormholes artificially.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Visualization_technique">Visualization technique</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wormhole&action=edit&section=1" title="Edit section: Visualization technique"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For a simplified notion of a wormhole, <a href="/wiki/Space" title="Space">space</a> can be visualized as a two-dimensional surface. In this case, a wormhole would appear as a hole in that surface, lead into a <a href="/wiki/Three-dimensional_space" title="Three-dimensional space">3D</a> tube (the inside surface of a <a href="/wiki/Cylinder" title="Cylinder">cylinder</a>), then re-emerge at another location on the 2D surface with a hole similar to the entrance. An actual wormhole would be analogous to this, but with the spatial dimensions raised by one. For example, instead of circular holes on a <a href="/wiki/2D_plane" class="mw-redirect" title="2D plane">2-Dimensional plane</a>, the entry and exit points could be visualized as spherical holes in <a href="/wiki/3D_space" class="mw-redirect" title="3D space">3D space</a> leading into a four-dimensional "tube" similar to a <a href="/wiki/Spherinder" title="Spherinder">spherinder</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (August 2023)">citation needed</span></a></i>]</sup> </p><p>Another way to imagine wormholes is to take a sheet of paper and draw two somewhat distant points on one side of the paper. The sheet of paper represents a plane in the <a href="/wiki/Spacetime" title="Spacetime">spacetime continuum</a>, and the two points represent a distance to be traveled, but theoretically, a wormhole could connect these two points by folding that plane (⁠<i>i.e.</i> the paper) so the points are touching. In this way, it would be much easier to traverse the distance since the two points are now touching. <sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (February 2025)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="Terminology">Terminology</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wormhole&action=edit&section=2" title="Edit section: Terminology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1928, German mathematician, philosopher and theoretical physicist <a href="/wiki/Hermann_Weyl" title="Hermann Weyl">Hermann Weyl</a> proposed a wormhole hypothesis of matter in connection with mass analysis of <a href="/wiki/Electromagnetic_field" title="Electromagnetic field">electromagnetic field</a> energy;<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> however, he did not use the term "wormhole" (he spoke of "one-dimensional tubes" instead).<sup id="cite_ref-SEP_9-0" class="reference"><a href="#cite_note-SEP-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>American <a href="/wiki/Theoretical_physicist" class="mw-redirect" title="Theoretical physicist">theoretical physicist</a> <a href="/wiki/John_Archibald_Wheeler" title="John Archibald Wheeler">John Archibald Wheeler</a> (inspired by Weyl's work)<sup id="cite_ref-SEP_9-1" class="reference"><a href="#cite_note-SEP-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> coined the term "wormhole".<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> In a 1957 paper that he wrote with <a href="/wiki/Charles_W._Misner" title="Charles W. Misner">Charles W. Misner</a>, they write:<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>This analysis forces one to consider situations ... where there is a net flux of lines of force, through what <a href="/wiki/Topologist" class="mw-redirect" title="Topologist">topologists</a> would call "a <a href="/wiki/Handle_decomposition" title="Handle decomposition">handle</a>" of the multiply-connected space, and what physicists might perhaps be excused for more vividly terming a "wormhole".</p><div class="templatequotecite">— <cite>Charles Misner and John Wheeler in <i><a href="/wiki/Annals_of_Physics" title="Annals of Physics">Annals of Physics</a></i></cite></div></blockquote> <div class="mw-heading mw-heading3"><h3 id="Modern_definitions">Modern definitions</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wormhole&action=edit&section=3" title="Edit section: Modern definitions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Wormholes have been defined both<a href="/wiki/Geometry_and_topology" title="Geometry and topology"><i> geometrically</i> and <i>topologically</i></a>. <sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag needs further explanation. (March 2017)">further explanation needed</span></a></i>]</sup> From a topological point of view, an intra-universe wormhole (a wormhole between two points in the same universe) is a <a href="/wiki/Compact_space" title="Compact space">compact</a> region of spacetime whose boundary is topologically trivial, but whose interior is not <a href="/wiki/Simply_connected" class="mw-redirect" title="Simply connected">simply connected</a>. Formalizing this idea leads to definitions such as the following, taken from Matt Visser's <i>Lorentzian Wormholes</i> (1996).<sup id="cite_ref-Visser1996_13-0" class="reference"><a href="#cite_note-Visser1996-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (January 2018)">page needed</span></a></i>]</sup> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>If a <a href="/wiki/Minkowski_space" title="Minkowski space">Minkowski spacetime</a> contains a compact region Ω, and if the topology of Ω is of the form Ω ~ S × Σ, where Σ is a three-manifold of the nontrivial topology, whose boundary has the topology of the form ∂Σ ~ S<sup>2</sup>, and if, furthermore, the <a href="/wiki/Hypersurface" title="Hypersurface">hypersurfaces</a> Σ are all spacelike, then the region Ω contains a quasi-permanent intrauniverse wormhole.</p></blockquote><p> Geometrically, wormholes can be described as regions of spacetime that constrain the incremental deformation of closed surfaces. For example, in Enrico Rodrigo's <i>The Physics of Stargates, </i>a wormhole is defined informally as: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"></p><blockquote class="templatequote"><p>a region of spacetime containing a "<a href="/wiki/World_tube" class="mw-redirect" title="World tube">world tube</a>" (the time evolution of a closed surface) that cannot be <a href="/wiki/Homotopy" title="Homotopy">continuously deformed</a> (shrunk) to a <a href="/wiki/World_line" title="World line">world line</a> (the time evolution of a point or observer).</p></blockquote> <div class="mw-heading mw-heading2"><h2 id="Development">Development</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wormhole&action=edit&section=4" title="Edit section: Development"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Lorentzian_Wormhole.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Lorentzian_Wormhole.svg/220px-Lorentzian_Wormhole.svg.png" decoding="async" width="220" height="213" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Lorentzian_Wormhole.svg/330px-Lorentzian_Wormhole.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Lorentzian_Wormhole.svg/440px-Lorentzian_Wormhole.svg.png 2x" data-file-width="620" data-file-height="600" /></a><figcaption>"Embedding diagram" of a Schwarzschild wormhole</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Schwarzschild_wormholes">Schwarzschild wormholes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wormhole&action=edit&section=5" title="Edit section: Schwarzschild wormholes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The first type of wormhole solution discovered was the Schwarzschild wormhole, which would be present in the <a href="/wiki/Schwarzschild_metric" title="Schwarzschild metric">Schwarzschild metric</a> describing an <i>eternal black hole</i>, but it was found that it would collapse too quickly for anything to cross from one end to the other. Wormholes that could be crossed in both directions, known as <a href="#Traversable_wormholes">traversable wormholes</a>, were thought to be possible only if <a href="/wiki/Exotic_matter" title="Exotic matter">exotic matter</a> with <a href="/wiki/Negative_energy" title="Negative energy">negative energy</a> <a href="/wiki/Energy_density" title="Energy density">density</a> could be used to stabilize them.<sup id="cite_ref-Rodrigo2_14-0" class="reference"><a href="#cite_note-Rodrigo2-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> However, physicists later reported that microscopic traversable wormholes may be possible and not require any exotic matter, instead requiring only <a href="/wiki/Electrically_charged" class="mw-redirect" title="Electrically charged">electrically charged</a> <a href="/wiki/Fermion" title="Fermion">fermionic</a> matter with small enough mass that it cannot collapse into a <a href="/wiki/Charged_black_hole" title="Charged black hole">charged black hole</a>.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> While such wormholes, if possible, may be limited to transfers of information, humanly traversable wormholes may exist if reality can broadly be described by the <a href="/wiki/Randall%E2%80%93Sundrum_model" title="Randall–Sundrum model">Randall–Sundrum model 2</a>, a <a href="/wiki/Brane" title="Brane">brane</a>-based theory consistent with <a href="/wiki/String_theory" title="String theory">string theory</a>.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Einstein–Rosen_bridges"><span id="Einstein.E2.80.93Rosen_bridges"></span>Einstein–Rosen bridges</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wormhole&action=edit&section=6" title="Edit section: Einstein–Rosen bridges"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Einstein–Rosen bridges</b> (or <b>ER bridges</b>),<sup id="cite_ref-Dobrev_20-0" class="reference"><a href="#cite_note-Dobrev-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> named after <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> and <a href="/wiki/Nathan_Rosen" title="Nathan Rosen">Nathan Rosen</a>,<sup id="cite_ref-ER_21-0" class="reference"><a href="#cite_note-ER-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> are connections between areas of space that can be modeled as <a href="/wiki/Vacuum_solution" class="mw-redirect" title="Vacuum solution">vacuum solutions</a> to the <a href="/wiki/Einstein_field_equations" title="Einstein field equations">Einstein field equations</a>, and that are now understood to be intrinsic parts of the <a href="/wiki/Kruskal%E2%80%93Szekeres_coordinates#The_maximally_extended_Schwarzschild_solution" title="Kruskal–Szekeres coordinates">maximally extended</a> version of the <a href="/wiki/Schwarzschild_metric" title="Schwarzschild metric">Schwarzschild metric</a> describing an eternal black hole with no charge and no rotation. Here, "maximally extended" refers to the idea that the <a href="/wiki/Spacetime" title="Spacetime">spacetime</a> should not have any "edges": it should be possible to continue this path arbitrarily far into the particle's future or past for any possible trajectory of a free-falling particle (following a <a href="/wiki/Geodesics_in_general_relativity" title="Geodesics in general relativity">geodesic</a> in the spacetime). </p><p>In order to satisfy this requirement, it turns out that in addition to the black hole interior region that particles enter when they fall through the <a href="/wiki/Event_horizon" title="Event horizon">event horizon</a> from the outside, there must be a separate <a href="/wiki/White_hole" title="White hole">white hole</a> interior region that allows us to extrapolate the trajectories of particles that an outside observer sees rising up <i>away</i> from the event horizon.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> And just as there are two separate interior regions of the maximally extended spacetime, there are also two separate exterior regions, sometimes called two different "universes", with the second universe allowing us to extrapolate some possible particle trajectories in the two interior regions. This means that the interior black hole region can contain a mix of particles that fell in from either universe (and thus an observer who fell in from one universe might be able to see the light that fell in from the other one), and likewise particles from the interior white hole region can escape into either universe. All four regions can be seen in a spacetime diagram that uses <a href="/wiki/Kruskal%E2%80%93Szekeres_coordinates" title="Kruskal–Szekeres coordinates">Kruskal–Szekeres coordinates</a>. </p><p>In this spacetime, it is possible to come up with <a href="/wiki/Coordinate_system" title="Coordinate system">coordinate systems</a> such that if a <a href="/wiki/Hypersurface" title="Hypersurface">hypersurface</a> of constant time (a set of points that all have the same time coordinate, such that every point on the surface has a <a href="/wiki/Space-like" class="mw-redirect" title="Space-like">space-like</a> separation, giving what is called a 'space-like surface') is picked and an "embedding diagram" drawn depicting the curvature of space at that time, the embedding diagram will look like a tube connecting the two exterior regions, known as an "Einstein–Rosen bridge". The Schwarzschild metric describes an idealized black hole that exists eternally from the perspective of external observers; a more realistic black hole that forms at some particular time from a collapsing star would require a different metric. When the infalling stellar matter is added to a diagram of a black hole's geography, it removes the part of the diagram corresponding to the white hole interior region, along with the part of the diagram corresponding to the other universe.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p><p>The Einstein–Rosen bridge was discovered by <a href="/wiki/Ludwig_Flamm" title="Ludwig Flamm">Ludwig Flamm</a> in 1916,<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> a few months after Schwarzschild published his solution, and was rediscovered by Albert Einstein and his colleague Nathan Rosen, who published their result in 1935.<sup id="cite_ref-ER_21-1" class="reference"><a href="#cite_note-ER-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-focus032505_25-0" class="reference"><a href="#cite_note-focus032505-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> However, in 1962, <a href="/wiki/John_Archibald_Wheeler" title="John Archibald Wheeler">John Archibald Wheeler</a> and <a href="/wiki/Robert_W._Fuller" title="Robert W. Fuller">Robert W. Fuller</a> published a paper<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> showing that this type of wormhole is unstable if it connects two parts of the same universe, and that it will pinch off too quickly for light (or any particle moving slower than light) that falls in from one exterior region to make it to the other exterior region. </p><p>According to general relativity, the <a href="/wiki/Gravitational_collapse" title="Gravitational collapse">gravitational collapse</a> of a sufficiently compact mass forms a singular Schwarzschild black hole. In the <a href="/wiki/Einstein%E2%80%93Cartan_theory" title="Einstein–Cartan theory">Einstein–Cartan</a>–Sciama–Kibble theory of gravity, however, it forms a regular Einstein–Rosen bridge. This theory extends general relativity by removing a constraint of the symmetry of the <a href="/wiki/Affine_connection" title="Affine connection">affine connection</a> and regarding its antisymmetric part, the <a href="/wiki/Torsion_tensor" title="Torsion tensor">torsion tensor</a>, as a dynamic variable. Torsion naturally accounts for the quantum-mechanical, intrinsic angular momentum (<a href="/wiki/Spin_(physics)" title="Spin (physics)">spin</a>) of matter. The minimal coupling between torsion and <a href="/wiki/Dirac_spinor" title="Dirac spinor">Dirac spinors</a> generates a repulsive spin–spin interaction that is significant in fermionic matter at extremely high densities. Such an interaction prevents the formation of a gravitational singularity (e.g. a black hole). Instead, the collapsing matter reaches an enormous but finite density and rebounds, forming the other side of the bridge.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p><p>Although Schwarzschild wormholes are not traversable in both directions, their existence inspired <a href="/wiki/Kip_Thorne" title="Kip Thorne">Kip Thorne</a> to imagine traversable wormholes created by holding the "throat" of a Schwarzschild wormhole open with <a href="/wiki/Exotic_matter" title="Exotic matter">exotic matter</a> (material that has negative mass/energy).<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p><p>Other non-traversable wormholes include <i>Lorentzian wormholes</i> (first proposed by John Archibald Wheeler in 1957), wormholes creating a <a href="/wiki/Spacetime_foam" class="mw-redirect" title="Spacetime foam">spacetime foam</a> in a general relativistic spacetime manifold depicted by a <a href="/wiki/Lorentzian_manifold" class="mw-redirect" title="Lorentzian manifold">Lorentzian manifold</a>,<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> and <i>Euclidean wormholes</i> (named after <a href="/wiki/Euclidean_manifold" class="mw-redirect" title="Euclidean manifold">Euclidean manifold</a>, a structure of <a href="/wiki/Riemannian_manifold" title="Riemannian manifold">Riemannian manifold</a>).<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Traversable_wormholes">Traversable wormholes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wormhole&action=edit&section=7" title="Edit section: Traversable wormholes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Casimir_effect" title="Casimir effect">Casimir effect</a> shows that <a href="/wiki/Quantum_field_theory" title="Quantum field theory">quantum field theory</a> allows the energy density in certain regions of space to be negative relative to the ordinary matter <a href="/wiki/Vacuum_energy" title="Vacuum energy">vacuum energy</a>, and it has been shown theoretically that quantum field theory allows states where energy can be <i>arbitrarily</i> <a href="/wiki/Negative_energy" title="Negative energy">negative</a> at a given point.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> Many physicists, such as <a href="/wiki/Stephen_Hawking" title="Stephen Hawking">Stephen Hawking</a>,<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Kip_Thorne" title="Kip Thorne">Kip Thorne</a>,<sup id="cite_ref-time_travel_33-0" class="reference"><a href="#cite_note-time_travel-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> and others,<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> argued that such effects might make it possible to stabilize a traversable wormhole.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> The only known natural process that is theoretically predicted to form a wormhole in the context of general relativity and quantum mechanics was put forth by <a href="/wiki/Juan_Maldacena" title="Juan Maldacena">Juan Maldacena</a> and <a href="/wiki/Leonard_Susskind" title="Leonard Susskind">Leonard Susskind</a> in their <a href="/wiki/ER_%3D_EPR" title="ER = EPR">ER = EPR</a> conjecture. The <a href="/wiki/Quantum_foam" title="Quantum foam">quantum foam</a> hypothesis is sometimes used to suggest that tiny wormholes might appear and disappear spontaneously at the <a href="/wiki/Planck_scale" class="mw-redirect" title="Planck scale">Planck scale</a>,<sup id="cite_ref-Thorne1994_38-0" class="reference"><a href="#cite_note-Thorne1994-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 494–496">: 494–496 </span></sup><sup id="cite_ref-quantumdynamics_39-0" class="reference"><a href="#cite_note-quantumdynamics-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> and stable versions of such wormholes have been suggested as <a href="/wiki/Dark_matter" title="Dark matter">dark matter</a> candidates.<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> It has also been proposed that, if a tiny wormhole held open by a <a href="/wiki/Negative_mass" title="Negative mass">negative mass</a> <a href="/wiki/Cosmic_string" title="Cosmic string">cosmic string</a> had appeared around the time of the <a href="/wiki/Big_Bang" title="Big Bang">Big Bang</a>, it could have been inflated to <a href="/wiki/Macroscopic_scale" title="Macroscopic scale">macroscopic</a> size by <a href="/wiki/Inflation_(cosmology)" class="mw-redirect" title="Inflation (cosmology)">cosmic inflation</a>.<sup id="cite_ref-naturalwormholes_42-0" class="reference"><a href="#cite_note-naturalwormholes-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Wurmloch.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/45/Wurmloch.jpg/220px-Wurmloch.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/45/Wurmloch.jpg/330px-Wurmloch.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/45/Wurmloch.jpg/440px-Wurmloch.jpg 2x" data-file-width="1024" data-file-height="768" /></a><figcaption>Image of a simulated traversable wormhole that connects the square in front of the physical institutes of <a href="/wiki/University_of_T%C3%BCbingen" title="University of Tübingen">University of Tübingen</a> with the sand dunes near <a href="/wiki/Boulogne-sur-Mer" title="Boulogne-sur-Mer">Boulogne-sur-Mer</a> in the north of France. The image is calculated with 4D <a href="/wiki/Ray_tracing_(graphics)" title="Ray tracing (graphics)">raytracing</a> in a Morris–Thorne wormhole metric, but the gravitational effects on the wavelength of light have not been simulated.<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>note 1<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>Lorentzian traversable wormholes would allow travel in both directions from one part of the universe to another part of that same universe very quickly or would allow travel from one universe to another. <span class="anchor" id="Ellis–Bronnikov_precedence"></span>The possibility of traversable wormholes in general relativity was first demonstrated in a 1973 paper by Homer Ellis<sup id="cite_ref-ellis1_44-0" class="reference"><a href="#cite_note-ellis1-44"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> and independently in a 1973 paper by K. A. Bronnikov.<sup id="cite_ref-bron_45-0" class="reference"><a href="#cite_note-bron-45"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> Ellis analyzed the topology and the <a href="/wiki/Geodesic" title="Geodesic">geodesics</a> of the <a href="/wiki/Ellis_drainhole" title="Ellis drainhole">Ellis drainhole</a>, showing it to be geodesically complete, horizonless, singularity-free, and fully traversable in both directions. The drainhole is a solution manifold of Einstein's field equations for a vacuum spacetime, modified by inclusion of a scalar field minimally coupled to the <a href="/wiki/Ricci_tensor" class="mw-redirect" title="Ricci tensor">Ricci tensor</a> with antiorthodox polarity (negative instead of positive). (Ellis specifically rejected referring to the scalar field as 'exotic' because of the antiorthodox coupling, finding arguments for doing so unpersuasive.) The solution depends on two parameters: <var style="padding-right: 1px;">m</var>, which fixes the strength of its gravitational field, and <var style="padding-right: 1px;">n</var>, which determines the curvature of its spatial cross sections. When <var style="padding-right: 1px;">m</var> is set equal to 0, the drainhole's gravitational field vanishes. What is left is the <a href="/wiki/Ellis_wormhole" title="Ellis wormhole">Ellis wormhole</a>, a nongravitating, purely geometric, traversable wormhole. </p><p><a href="/wiki/Kip_Thorne" title="Kip Thorne">Kip Thorne</a> and his graduate student <a href="/wiki/Mike_Morris_(physicist)" title="Mike Morris (physicist)">Mike Morris</a> independently discovered in 1988 the Ellis wormhole and argued for its use as a tool for teaching general relativity.<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> For this reason, the type of traversable wormhole they proposed, held open by a spherical shell of <a href="/wiki/Exotic_matter" title="Exotic matter">exotic matter</a>, is also known as a <i>Morris–Thorne wormhole</i>. </p><p>Later, other types of traversable wormholes were discovered as allowable solutions to the equations of general relativity, including a variety analyzed in a 1989 paper by Matt Visser, in which a path through the wormhole can be made where the traversing path does not pass through a region of exotic matter. However, in the pure <a href="/wiki/Gauss%E2%80%93Bonnet_gravity" title="Gauss–Bonnet gravity">Gauss–Bonnet gravity</a> (a modification to general relativity involving extra spatial dimensions which is sometimes studied in the context of <a href="/wiki/Brane_cosmology" title="Brane cosmology">brane cosmology</a>) exotic matter is not needed in order for wormholes to exist—they can exist even with no matter.<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> A type held open by negative mass <a href="/wiki/Cosmic_string" title="Cosmic string">cosmic strings</a> was put forth by Visser in collaboration with <a href="/wiki/John_G._Cramer" title="John G. Cramer">Cramer</a> <i>et al.</i>,<sup id="cite_ref-naturalwormholes_42-1" class="reference"><a href="#cite_note-naturalwormholes-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> in which it was proposed that such wormholes could have been naturally created in the early universe. </p><p>Wormholes connect two points in spacetime, which means that they would in principle allow <a href="/wiki/Time_travel" title="Time travel">travel in time</a>, as well as in space. In 1988, Morris, Thorne and Yurtsever worked out how to convert a wormhole traversing space into one traversing time by accelerating one of its two mouths.<sup id="cite_ref-time_travel_33-1" class="reference"><a href="#cite_note-time_travel-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> However, according to general relativity, it would not be possible to use a wormhole to travel back to a time earlier than when the wormhole was first converted into a time "machine". Until this time it could not have been noticed or have been used.<sup id="cite_ref-Thorne1994_38-1" class="reference"><a href="#cite_note-Thorne1994-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 504">: 504 </span></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Raychaudhuri's_theorem_and_exotic_matter"><span id="Raychaudhuri.27s_theorem_and_exotic_matter"></span>Raychaudhuri's theorem and exotic matter</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wormhole&action=edit&section=8" title="Edit section: Raychaudhuri's theorem and exotic matter"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>To see why <a href="/wiki/Exotic_matter" title="Exotic matter">exotic matter</a> is required, consider an incoming light front traveling along geodesics, which then crosses the wormhole and re-expands on the other side. The <a href="/wiki/Congruence_(general_relativity)" title="Congruence (general relativity)">expansion</a> goes from negative to positive. As the wormhole neck is of finite size, we would not expect caustics to develop, at least within the vicinity of the neck. According to the optical <a href="/wiki/Raychaudhuri%27s_theorem" class="mw-redirect" title="Raychaudhuri's theorem">Raychaudhuri's theorem</a>, this requires a violation of the <a href="/wiki/Averaged_null_energy_condition" class="mw-redirect" title="Averaged null energy condition">averaged null energy condition</a>. Quantum effects such as the <a href="/wiki/Casimir_effect" title="Casimir effect">Casimir effect</a> cannot violate the averaged null energy condition in any neighborhood of space with zero curvature,<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> but calculations in <a href="/wiki/Semiclassical_gravity" title="Semiclassical gravity">semiclassical gravity</a> suggest that quantum effects may be able to violate this condition in curved spacetime.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> Although it was hoped recently that quantum effects could not violate an achronal version of the averaged null energy condition,<sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> violations have nevertheless been found,<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> so it remains an open possibility that quantum effects might be used to support a wormhole. </p> <div class="mw-heading mw-heading2"><h2 id="Modified_general_relativity">Modified general relativity</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wormhole&action=edit&section=9" title="Edit section: Modified general relativity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In some hypotheses where <a href="/wiki/Alternatives_to_general_relativity" title="Alternatives to general relativity">general relativity is modified</a>, it is possible to have a wormhole that does not collapse without having to resort to exotic matter. For example, this is possible with R<sup>2</sup> gravity, a form of <a href="/wiki/F(R)_gravity" title="F(R) gravity"><var style="padding-right: 1px;">f</var>(<var style="padding-right: 1px;">R</var>) gravity</a>.<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Faster-than-light_travel">Faster-than-light travel</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wormhole&action=edit&section=10" title="Edit section: Faster-than-light travel"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Faster-than-light" title="Faster-than-light">Faster-than-light</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Wormhole_travel_as_envisioned_by_Les_Bossinas_for_NASA.jpg" class="mw-file-description"><img alt="Wormhole travel as envisioned by Les Bossinas for NASA Digital art by Les Bossinas (Cortez III Service Corp.), 1998" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Wormhole_travel_as_envisioned_by_Les_Bossinas_for_NASA.jpg/220px-Wormhole_travel_as_envisioned_by_Les_Bossinas_for_NASA.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Wormhole_travel_as_envisioned_by_Les_Bossinas_for_NASA.jpg/330px-Wormhole_travel_as_envisioned_by_Les_Bossinas_for_NASA.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/70/Wormhole_travel_as_envisioned_by_Les_Bossinas_for_NASA.jpg/440px-Wormhole_travel_as_envisioned_by_Les_Bossinas_for_NASA.jpg 2x" data-file-width="1200" data-file-height="900" /></a><figcaption>Wormhole travel as envisioned by Les Bossinas for <a href="/wiki/NASA" title="NASA">NASA</a>, <abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 1998</span></figcaption></figure> <p>The impossibility of faster-than-light relative speed applies only locally. Wormholes might allow effective superluminal (<a href="/wiki/Faster-than-light" title="Faster-than-light">faster-than-light</a>) travel by ensuring that the speed of light is not exceeded locally at any time. While traveling through a wormhole, subluminal (slower-than-light) speeds are used. If two points are connected by a wormhole whose length is shorter than the distance between them <i>outside</i> the wormhole, the time taken to traverse it could be less than the time it would take a light beam to make the journey if it took a path through the space <i>outside</i> the wormhole. However, a light beam traveling through the same wormhole would beat the traveler. </p> <div class="mw-heading mw-heading2"><h2 id="Time_travel">Time travel</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wormhole&action=edit&section=11" title="Edit section: Time travel"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Time_travel" title="Time travel">Time travel</a></div> <p>If <a href="#Traversable_wormholes">traversable wormholes</a> exist, they might allow <a href="/wiki/Time_travel" title="Time travel">time travel</a>.<sup id="cite_ref-time_travel_33-2" class="reference"><a href="#cite_note-time_travel-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> A proposed time-travel machine using a traversable wormhole might hypothetically work in the following way: One end of the wormhole is accelerated to some significant fraction of the speed of light, perhaps with some advanced <a href="/wiki/Vehicle_propulsion" class="mw-redirect" title="Vehicle propulsion">propulsion system</a>, and then brought back to the point of origin. Alternatively, another way is to take one entrance of the wormhole and move it to within the gravitational field of an object that has higher gravity than the other entrance, and then return it to a position near the other entrance. For both these methods, <a href="/wiki/Time_dilation" title="Time dilation">time dilation</a> causes the end of the wormhole that has been moved to have aged less, or become "younger", than the stationary end as seen by an external observer; however, time connects differently <i>through</i> the wormhole than <i>outside</i> it, so that <a href="/wiki/Synchronization" title="Synchronization">synchronized</a> clocks at either end of the wormhole will always remain synchronized as seen by an observer passing through the wormhole, no matter how the two ends move around.<sup id="cite_ref-Thorne1994_38-2" class="reference"><a href="#cite_note-Thorne1994-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 502">: 502 </span></sup> This means that an observer entering the "younger" end would exit the "older" end at a time when it was the same age as the "younger" end, effectively going back in time as seen by an observer from the outside. One significant limitation of such a time machine is that it is only possible to go as far back in time as the initial creation of the machine;<sup id="cite_ref-Thorne1994_38-3" class="reference"><a href="#cite_note-Thorne1994-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 503">: 503 </span></sup> it is more of a path through time rather than it is a device that itself moves through time, and it would not allow the technology itself to be moved backward in time.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> </p><p>According to current theories on the nature of wormholes, construction of a traversable wormhole would require the existence of a substance with negative energy, often referred to as "<a href="/wiki/Exotic_matter" title="Exotic matter">exotic matter</a>". More technically, the wormhole spacetime requires a distribution of energy that violates various <a href="/wiki/Energy_condition" title="Energy condition">energy conditions</a>, such as the null energy condition along with the weak, strong, and dominant energy conditions. However, it is known that quantum effects can lead to small measurable violations of the null energy condition,<sup id="cite_ref-Visser1996_13-1" class="reference"><a href="#cite_note-Visser1996-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 101">: 101 </span></sup> and many physicists believe that the required negative energy may actually be possible due to the <a href="/wiki/Casimir_effect" title="Casimir effect">Casimir effect</a> in quantum physics.<sup id="cite_ref-casimir_55-0" class="reference"><a href="#cite_note-casimir-55"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> Although early calculations suggested a very large amount of negative energy would be required, later calculations showed that the amount of negative energy can be made arbitrarily small.<sup id="cite_ref-negative_energy_56-0" class="reference"><a href="#cite_note-negative_energy-56"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> </p><p>In 1993, Matt Visser argued that the two mouths of a wormhole with such an induced clock difference could not be brought together without inducing quantum field and gravitational effects that would either make the wormhole collapse or the two mouths repel each other,<sup id="cite_ref-visser_1_57-0" class="reference"><a href="#cite_note-visser_1-57"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> or otherwise prevent information from passing through the wormhole.<sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> Because of this, the two mouths could not be brought close enough for <a href="/wiki/Causality_(physics)" title="Causality (physics)">causality</a> violation to take place. However, in a 1997 paper, Visser hypothesized that a complex "<a href="/wiki/Roman_ring" title="Roman ring">Roman ring</a>" (named after Tom Roman) configuration of an N number of wormholes arranged in a symmetric polygon could still act as a time machine, although he concludes that this is more likely a flaw in classical quantum gravity theory rather than proof that causality violation is possible.<sup id="cite_ref-visser_2_59-0" class="reference"><a href="#cite_note-visser_2-59"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Interuniversal_travel">Interuniversal travel</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wormhole&action=edit&section=12" title="Edit section: Interuniversal travel"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Multiverse" title="Multiverse">Multiverse</a></div> <p>A possible resolution to the paradoxes resulting from wormhole-enabled time travel rests on the <a href="/wiki/Many-worlds_interpretation" title="Many-worlds interpretation">many-worlds interpretation</a> of <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>. </p><p>In 1991 <a href="/wiki/David_Deutsch" title="David Deutsch">David Deutsch</a> showed that quantum theory is fully consistent (in the sense that the so-called <a href="/wiki/Density_matrix" title="Density matrix">density matrix</a> can be made free of discontinuities) in spacetimes with closed timelike curves.<sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup> However, later it was shown that such a model of closed timelike curves can have internal inconsistencies as it will lead to strange phenomena like distinguishing non-orthogonal quantum states and distinguishing proper and improper mixture.<sup id="cite_ref-61" class="reference"><a href="#cite_note-61"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> Accordingly, the destructive positive feedback loop of virtual particles circulating through a wormhole time machine, a result indicated by semi-classical calculations, is averted. A particle returning from the future does not return to its universe of origination but to a parallel universe. This suggests that a wormhole time machine with an exceedingly short time jump is a theoretical bridge between contemporaneous parallel universes.<sup id="cite_ref-Rodrigo2_14-1" class="reference"><a href="#cite_note-Rodrigo2-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>Because a wormhole time-machine introduces a type of nonlinearity into quantum theory, this sort of communication between parallel universes is consistent with <a href="/wiki/Joseph_Polchinski" title="Joseph Polchinski">Joseph Polchinski</a>'s proposal of an <b>Everett phone</b><sup id="cite_ref-63" class="reference"><a href="#cite_note-63"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> (named after <a href="/wiki/Hugh_Everett_III" title="Hugh Everett III">Hugh Everett</a>) in <a href="/wiki/Steven_Weinberg" title="Steven Weinberg">Steven Weinberg</a>'s formulation of nonlinear quantum mechanics.<sup id="cite_ref-64" class="reference"><a href="#cite_note-64"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> </p><p>The possibility of communication between parallel universes has been dubbed <b>interuniversal travel</b>.<sup id="cite_ref-65" class="reference"><a href="#cite_note-65"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> </p><p>Wormhole can also be depicted in a <a href="/wiki/Penrose_diagram" title="Penrose diagram">Penrose diagram</a> of a <a href="/wiki/Schwarzschild_Black_Hole" class="mw-redirect" title="Schwarzschild Black Hole">Schwarzschild black hole</a>. In the Penrose diagram, an object traveling faster than light will cross the black hole and will emerge from another end into a different space, time or universe. This will be an inter-universal wormhole. </p> <div class="mw-heading mw-heading2"><h2 id="Metrics">Metrics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wormhole&action=edit&section=13" title="Edit section: Metrics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Theories of <i>wormhole metrics</i> describe the spacetime geometry of a wormhole and serve as theoretical models for time travel. An example of a (traversable) wormhole <a href="/wiki/Metric_tensor" title="Metric tensor">metric</a> is the following:<sup id="cite_ref-66" class="reference"><a href="#cite_note-66"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup> </p> <style data-mw-deduplicate="TemplateStyles:r996643573">.mw-parser-output .block-indent{padding-left:3em;padding-right:0;overflow:hidden}</style><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ds^{2}=-c^{2}\,dt^{2}+d\ell ^{2}+(k^{2}+\ell ^{2})(d\theta ^{2}+\sin ^{2}\theta \,d\varphi ^{2}),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mi>d</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>d</mi> <msup> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <msup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>d</mi> <msup> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>θ</mi> <mspace width="thinmathspace" /> <mi>d</mi> <msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ds^{2}=-c^{2}\,dt^{2}+d\ell ^{2}+(k^{2}+\ell ^{2})(d\theta ^{2}+\sin ^{2}\theta \,d\varphi ^{2}),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7dc7d81a79c091258173e9d59da6d3d93326b102" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:49.907ex; height:3.176ex;" alt="{\displaystyle ds^{2}=-c^{2}\,dt^{2}+d\ell ^{2}+(k^{2}+\ell ^{2})(d\theta ^{2}+\sin ^{2}\theta \,d\varphi ^{2}),}"></span></div> <p>first presented by Ellis (see <a href="/wiki/Ellis_wormhole" title="Ellis wormhole">Ellis wormhole</a>) as a special case of the <a href="/wiki/Ellis_drainhole" title="Ellis drainhole">Ellis drainhole</a>. </p><p>One type of non-traversable wormhole <a href="/wiki/Metric_tensor" title="Metric tensor">metric</a> is the <a href="/wiki/Schwarzschild_metric" title="Schwarzschild metric">Schwarzschild solution</a> (see the first diagram): </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ds^{2}=-c^{2}\left(1-{\frac {2GM}{rc^{2}}}\right)\,dt^{2}+{\frac {dr^{2}}{1-{\frac {2GM}{rc^{2}}}}}+r^{2}(d\theta ^{2}+\sin ^{2}\theta \,d\varphi ^{2}).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>G</mi> <mi>M</mi> </mrow> <mrow> <mi>r</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>G</mi> <mi>M</mi> </mrow> <mrow> <mi>r</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> </mfrac> </mrow> <mo>+</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>d</mi> <msup> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>θ</mi> <mspace width="thinmathspace" /> <mi>d</mi> <msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ds^{2}=-c^{2}\left(1-{\frac {2GM}{rc^{2}}}\right)\,dt^{2}+{\frac {dr^{2}}{1-{\frac {2GM}{rc^{2}}}}}+r^{2}(d\theta ^{2}+\sin ^{2}\theta \,d\varphi ^{2}).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a370ed8fed648239c227a9dd115c7046c5e98ef9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.838ex; width:63.812ex; height:7.676ex;" alt="{\displaystyle ds^{2}=-c^{2}\left(1-{\frac {2GM}{rc^{2}}}\right)\,dt^{2}+{\frac {dr^{2}}{1-{\frac {2GM}{rc^{2}}}}}+r^{2}(d\theta ^{2}+\sin ^{2}\theta \,d\varphi ^{2}).}"></span></div> <p>The original Einstein–Rosen bridge was described in an article published in July 1935.<sup id="cite_ref-67" class="reference"><a href="#cite_note-67"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-68" class="reference"><a href="#cite_note-68"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup> </p><p>For the Schwarzschild spherically symmetric static solution </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ds^{2}=-{\frac {1}{1-{\frac {2m}{r}}}}\,dr^{2}-r^{2}(d\theta ^{2}+\sin ^{2}\theta \,d\varphi ^{2})+\left(1-{\frac {2m}{r}}\right)\,dt^{2},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>m</mi> </mrow> <mi>r</mi> </mfrac> </mrow> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>d</mi> <msup> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>θ</mi> <mspace width="thinmathspace" /> <mi>d</mi> <msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>m</mi> </mrow> <mi>r</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ds^{2}=-{\frac {1}{1-{\frac {2m}{r}}}}\,dr^{2}-r^{2}(d\theta ^{2}+\sin ^{2}\theta \,d\varphi ^{2})+\left(1-{\frac {2m}{r}}\right)\,dt^{2},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45ea92b9018f59f310ccd407f18410b188f8a807" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:61.265ex; height:7.009ex;" alt="{\displaystyle ds^{2}=-{\frac {1}{1-{\frac {2m}{r}}}}\,dr^{2}-r^{2}(d\theta ^{2}+\sin ^{2}\theta \,d\varphi ^{2})+\left(1-{\frac {2m}{r}}\right)\,dt^{2},}"></span></div> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ds}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ds}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f0fb36e4308227d3e4a1f809c2571ec02527100" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.306ex; height:2.176ex;" alt="{\displaystyle ds}"></span> is the proper time and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3e3467f9e219a5ea38a30da5c3a02c2c23f61a79" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.268ex; height:2.176ex;" alt="{\displaystyle c=1}"></span>. </p><p>If one replaces <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span> with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e6bb763d22c20916ed4f0bb6bd49d7470cffd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle u}"></span> according to <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u^{2}=r-2m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>r</mi> <mo>−</mo> <mn>2</mn> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u^{2}=r-2m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64a75f02310cccd0b7fc4824995347d06456bc78" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.574ex; height:2.843ex;" alt="{\displaystyle u^{2}=r-2m}"></span> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ds^{2}=-4(u^{2}+2m)\,du^{2}-(u^{2}+2m)^{2}(d\theta ^{2}+\sin ^{2}\theta \,d\varphi ^{2})+{\frac {u^{2}}{u^{2}+2m}}\,dt^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo>−</mo> <mn>4</mn> <mo stretchy="false">(</mo> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi>m</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mo stretchy="false">(</mo> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi>m</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>d</mi> <msup> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>θ</mi> <mspace width="thinmathspace" /> <mi>d</mi> <msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi>m</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ds^{2}=-4(u^{2}+2m)\,du^{2}-(u^{2}+2m)^{2}(d\theta ^{2}+\sin ^{2}\theta \,d\varphi ^{2})+{\frac {u^{2}}{u^{2}+2m}}\,dt^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9448be6efa66028c3fb6e2c9bafda84e6e92f493" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:70.96ex; height:6.176ex;" alt="{\displaystyle ds^{2}=-4(u^{2}+2m)\,du^{2}-(u^{2}+2m)^{2}(d\theta ^{2}+\sin ^{2}\theta \,d\varphi ^{2})+{\frac {u^{2}}{u^{2}+2m}}\,dt^{2}}"></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>The four-dimensional space is described mathematically by two congruent parts or "sheets", corresponding to <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e02252ee214e4ce9f8e8add664b786cbc55dd40c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.591ex; height:2.176ex;" alt="{\displaystyle u>0}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d92db92f7fcc3aa3e985f671c467f1d45cedd1c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.591ex; height:2.176ex;" alt="{\displaystyle u<0}"></span>, which are joined by a hyperplane <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r=2m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mn>2</mn> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=2m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/366d88363bbf1b038ab3c122ba08da023d09fdb3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.35ex; height:2.176ex;" alt="{\displaystyle r=2m}"></span> or <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41c2a269988ef0c55e0449b74950a4976e35a067" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.591ex; height:2.176ex;" alt="{\displaystyle u=0}"></span> in which <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3556280e66fe2c0d0140df20935a6f057381d77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.116ex; height:2.009ex;" alt="{\displaystyle g}"></span> vanishes. We call such a connection between the two sheets a "bridge".</p><div class="templatequotecite">— <cite>A. Einstein, N. Rosen, "The Particle Problem in the General Theory of Relativity"</cite></div></blockquote> <p>For the combined field, gravity and electricity, Einstein and Rosen derived the following Schwarzschild static spherically symmetric solution </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi _{1}=\varphi _{2}=\varphi _{3}=0,\varphi _{4}={\frac {\varepsilon }{4}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>,</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ε</mi> <mn>4</mn> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi _{1}=\varphi _{2}=\varphi _{3}=0,\varphi _{4}={\frac {\varepsilon }{4}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/991f809e785f14ca1bb4d21ca868c0c187984f51" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:27.533ex; height:4.676ex;" alt="{\displaystyle \varphi _{1}=\varphi _{2}=\varphi _{3}=0,\varphi _{4}={\frac {\varepsilon }{4}},}"></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ds^{2}=-{\frac {1}{\left(1-{\frac {2m}{r}}-{\frac {\varepsilon ^{2}}{2r^{2}}}\right)}}\,dr^{2}-r^{2}(d\theta ^{2}+\sin ^{2}\theta \,d\varphi ^{2})+\left(1-{\frac {2m}{r}}-{\frac {\varepsilon ^{2}}{2r^{2}}}\right)\,dt^{2},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>m</mi> </mrow> <mi>r</mi> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>d</mi> <msup> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>θ</mi> <mspace width="thinmathspace" /> <mi>d</mi> <msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>m</mi> </mrow> <mi>r</mi> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ds^{2}=-{\frac {1}{\left(1-{\frac {2m}{r}}-{\frac {\varepsilon ^{2}}{2r^{2}}}\right)}}\,dr^{2}-r^{2}(d\theta ^{2}+\sin ^{2}\theta \,d\varphi ^{2})+\left(1-{\frac {2m}{r}}-{\frac {\varepsilon ^{2}}{2r^{2}}}\right)\,dt^{2},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97228280bd7f1d45a1f9ce5f28b8255aa3bd39ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.505ex; width:77.054ex; height:8.343ex;" alt="{\displaystyle ds^{2}=-{\frac {1}{\left(1-{\frac {2m}{r}}-{\frac {\varepsilon ^{2}}{2r^{2}}}\right)}}\,dr^{2}-r^{2}(d\theta ^{2}+\sin ^{2}\theta \,d\varphi ^{2})+\left(1-{\frac {2m}{r}}-{\frac {\varepsilon ^{2}}{2r^{2}}}\right)\,dt^{2},}"></span></div> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varepsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ε</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a30c89172e5b88edbd45d3e2772c7f5e562e5173" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle \varepsilon }"></span> is the electric charge. </p><p>The field equations without denominators in the case when <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e57f21007575fd03e3be0da20af34d25829cc9a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.301ex; height:2.176ex;" alt="{\displaystyle m=0}"></span> can be written </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi _{\mu \nu }=\varphi _{\mu ,\nu }-\varphi _{\nu ,\mu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mo>,</mo> <mi>ν</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> <mo>,</mo> <mi>μ</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi _{\mu \nu }=\varphi _{\mu ,\nu }-\varphi _{\nu ,\mu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/26fa51a4aec154a98fdbfbac22b12dd2212af7f6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:17.698ex; height:2.676ex;" alt="{\displaystyle \varphi _{\mu \nu }=\varphi _{\mu ,\nu }-\varphi _{\nu ,\mu }}"></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g^{2}\varphi _{\mu \nu ;\sigma }g^{\nu \sigma }=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> <mo>;</mo> <mi>σ</mi> </mrow> </msub> <msup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> <mi>σ</mi> </mrow> </msup> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g^{2}\varphi _{\mu \nu ;\sigma }g^{\nu \sigma }=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8495f363375be4922a0cc4716b93290e2e5e1d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:14.608ex; height:3.343ex;" alt="{\displaystyle g^{2}\varphi _{\mu \nu ;\sigma }g^{\nu \sigma }=0}"></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g^{2}(R_{ik}+\varphi _{i\alpha }\varphi _{k}^{\alpha }-{\frac {1}{4}}g_{ik}\varphi _{\alpha \beta }\varphi ^{\alpha \beta })=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>α</mi> </mrow> </msub> <msubsup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msubsup> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>k</mi> </mrow> </msub> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msub> <msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g^{2}(R_{ik}+\varphi _{i\alpha }\varphi _{k}^{\alpha }-{\frac {1}{4}}g_{ik}\varphi _{\alpha \beta }\varphi ^{\alpha \beta })=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9cccc661f97704c1c241f18c446aeaede253fd3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:35.776ex; height:5.176ex;" alt="{\displaystyle g^{2}(R_{ik}+\varphi _{i\alpha }\varphi _{k}^{\alpha }-{\frac {1}{4}}g_{ik}\varphi _{\alpha \beta }\varphi ^{\alpha \beta })=0}"></span></div> <p>In order to eliminate singularities, if one replaces <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span> by <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e6bb763d22c20916ed4f0bb6bd49d7470cffd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle u}"></span> according to the equation: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u^{2}=r^{2}-{\frac {\varepsilon ^{2}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u^{2}=r^{2}-{\frac {\varepsilon ^{2}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/411d18c51b206719b9f972ed44a82d49560e7c8d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.4ex; height:5.676ex;" alt="{\displaystyle u^{2}=r^{2}-{\frac {\varepsilon ^{2}}{2}}}"></span></div> <p>and with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e57f21007575fd03e3be0da20af34d25829cc9a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.301ex; height:2.176ex;" alt="{\displaystyle m=0}"></span> one obtains<sup id="cite_ref-69" class="reference"><a href="#cite_note-69"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-70" class="reference"><a href="#cite_note-70"><span class="cite-bracket">[</span>69<span class="cite-bracket">]</span></a></sup> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi _{1}=\varphi _{2}=\varphi _{3}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi _{1}=\varphi _{2}=\varphi _{3}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ff2b40b712573a4de53bfc5f4aa115a2f0e621b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.181ex; height:2.676ex;" alt="{\displaystyle \varphi _{1}=\varphi _{2}=\varphi _{3}=0}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi _{4}={\frac {\varepsilon }{\left(u^{2}+{\frac {\varepsilon ^{2}}{2}}\right)^{1/2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ε</mi> <msup> <mrow> <mo>(</mo> <mrow> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi _{4}={\frac {\varepsilon }{\left(u^{2}+{\frac {\varepsilon ^{2}}{2}}\right)^{1/2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62784a4f50e6de4e505140411a85c6a94829e5e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.005ex; width:19.641ex; height:7.843ex;" alt="{\displaystyle \varphi _{4}={\frac {\varepsilon }{\left(u^{2}+{\frac {\varepsilon ^{2}}{2}}\right)^{1/2}}}}"></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ds^{2}=-du^{2}-\left(u^{2}+{\frac {\varepsilon ^{2}}{2}}\right)(d\theta ^{2}+\sin ^{2}\theta \,d\varphi ^{2})+\left({\frac {2u^{2}}{2u^{2}+\varepsilon ^{2}}}\right)\,dt^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo>−</mo> <mi>d</mi> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mrow> <mo>(</mo> <mrow> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo stretchy="false">(</mo> <mi>d</mi> <msup> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>θ</mi> <mspace width="thinmathspace" /> <mi>d</mi> <msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>+</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>2</mn> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ds^{2}=-du^{2}-\left(u^{2}+{\frac {\varepsilon ^{2}}{2}}\right)(d\theta ^{2}+\sin ^{2}\theta \,d\varphi ^{2})+\left({\frac {2u^{2}}{2u^{2}+\varepsilon ^{2}}}\right)\,dt^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37151e4140e845149c4d39dcf9005c7331d7bf04" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:63.795ex; height:6.343ex;" alt="{\displaystyle ds^{2}=-du^{2}-\left(u^{2}+{\frac {\varepsilon ^{2}}{2}}\right)(d\theta ^{2}+\sin ^{2}\theta \,d\varphi ^{2})+\left({\frac {2u^{2}}{2u^{2}+\varepsilon ^{2}}}\right)\,dt^{2}}"></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>The solution is free from singularities for all finite points in the space of the two sheets</p><div class="templatequotecite">— <cite>A. Einstein, N. Rosen, "The Particle Problem in the General Theory of Relativity"</cite></div></blockquote> <div class="mw-heading mw-heading2"><h2 id="In_fiction">In fiction</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wormhole&action=edit&section=14" title="Edit section: In fiction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Wormholes_in_fiction" title="Wormholes in fiction">Wormholes in fiction</a></div> <p>Wormholes are a common element in <a href="/wiki/Science_fiction" title="Science fiction">science fiction</a> because they allow interstellar, intergalactic, and sometimes even interuniversal travel within human lifetime scales. In fiction, wormholes have also served as a method for <a href="/wiki/Time_travel" title="Time travel">time travel</a>. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wormhole&action=edit&section=15" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1266661725">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/25px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="25" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/37px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/49px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-file-width="530" data-file-height="600" /></a></span></span><span class="portalbox-link"><a href="/wiki/Portal:Physics" title="Portal:Physics">Physics portal</a></span></li><li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:He1523a.jpg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/He1523a.jpg/24px-He1523a.jpg" decoding="async" width="24" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/He1523a.jpg/36px-He1523a.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5f/He1523a.jpg/49px-He1523a.jpg 2x" data-file-width="180" data-file-height="207" /></a></span></span><span class="portalbox-link"><a href="/wiki/Portal:Star" class="mw-redirect" title="Portal:Star">Star portal</a></span></li></ul> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 25em;"> <ul><li><a href="/wiki/Alcubierre_drive" title="Alcubierre drive">Alcubierre drive</a></li> <li><a href="/wiki/ER_%3D_EPR" title="ER = EPR">ER = EPR</a></li> <li><a href="/wiki/G%C3%B6del_metric" title="Gödel metric">Gödel metric</a></li> <li><a href="/wiki/Krasnikov_tube" title="Krasnikov tube">Krasnikov tube</a></li> <li><a href="/wiki/Non-orientable_wormhole" title="Non-orientable wormhole">Non-orientable wormhole</a></li> <li><a href="/wiki/Novikov_self-consistency_principle" title="Novikov self-consistency principle">Novikov self-consistency principle</a></li> <li><a href="/wiki/Polchinski%27s_paradox" class="mw-redirect" title="Polchinski's paradox">Polchinski's paradox</a></li> <li><a href="/wiki/Retrocausality" title="Retrocausality">Retrocausality</a></li> <li><a href="/wiki/Ring_singularity" title="Ring singularity">Ring singularity</a></li> <li><a href="/wiki/Roman_ring" title="Roman ring">Roman ring</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wormhole&action=edit&section=16" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-43">^</a></b></span> <span class="reference-text">Other computer-rendered images and animations of traversable wormholes can be seen on <a rel="nofollow" class="external text" href="http://www.spacetimetravel.org/wurmlochflug/wurmlochflug.html">this page</a> by the creator of the image in the article, and <a rel="nofollow" class="external text" href="https://web.archive.org/web/20151228145356/https://www.vis.uni-stuttgart.de/~muelleta/MTvis/">this page</a> has additional renderings.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wormhole&action=edit&section=17" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Citations">Citations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wormhole&action=edit&section=18" title="Edit section: Citations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-NYT-20221010-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-NYT-20221010_1-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFOverbye2022" class="citation news cs1"><a href="/wiki/Dennis_Overbye" title="Dennis Overbye">Overbye, Dennis</a> (10 October 2022). <a rel="nofollow" class="external text" href="https://www.nytimes.com/2022/10/10/science/black-holes-cosmology-hologram.html">"Black Holes May Hide a Mind-Bending Secret About Our Universe – Take gravity, add quantum mechanics, stir. What do you get? Just maybe, a holographic cosmos"</a>. <i><a href="/wiki/The_New_York_Times" title="The New York Times">The New York Times</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">10 October</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+New+York+Times&rft.atitle=Black+Holes+May+Hide+a+Mind-Bending+Secret+About+Our+Universe+%E2%80%93+Take+gravity%2C+add+quantum+mechanics%2C+stir.+What+do+you+get%3F+Just+maybe%2C+a+holographic+cosmos.&rft.date=2022-10-10&rft.aulast=Overbye&rft.aufirst=Dennis&rft_id=https%3A%2F%2Fwww.nytimes.com%2F2022%2F10%2F10%2Fscience%2Fblack-holes-cosmology-hologram.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShinkaiTorii2015" class="citation journal cs1">Shinkai, Hisa-aki; Torii, Takashi (2015-01-21). <a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F1742-6596%2F574%2F1%2F012056">"Wormhole Dynamics"</a>. <i>Journal of Physics: Conference Series</i>. <b>574</b>: 012056. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F1742-6596%2F574%2F1%2F012056">10.1088/1742-6596/574/1/012056</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1742-6588">1742-6588</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Physics%3A+Conference+Series&rft.atitle=Wormhole+Dynamics&rft.volume=574&rft.pages=012056&rft.date=2015-01-21&rft_id=info%3Adoi%2F10.1088%2F1742-6596%2F574%2F1%2F012056&rft.issn=1742-6588&rft.aulast=Shinkai&rft.aufirst=Hisa-aki&rft.au=Torii%2C+Takashi&rft_id=https%3A%2F%2Fdoi.org%2F10.1088%252F1742-6596%252F574%252F1%252F012056&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChoi2013" class="citation web cs1">Choi, Charles Q. (2013-12-03). <a rel="nofollow" class="external text" href="http://www.nbcnews.com/science/science-news/spooky-physics-phenomenon-may-link-universes-wormholes-f2D11690659">"Spooky physics phenomenon may link universe's wormholes"</a>. NBC News<span class="reference-accessdate">. Retrieved <span class="nowrap">2019-07-30</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Spooky+physics+phenomenon+may+link+universe%27s+wormholes&rft.pub=NBC+News&rft.date=2013-12-03&rft.aulast=Choi&rft.aufirst=Charles+Q.&rft_id=http%3A%2F%2Fwww.nbcnews.com%2Fscience%2Fscience-news%2Fspooky-physics-phenomenon-may-link-universes-wormholes-f2D11690659&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCramerForwardMorrisVisser1995" class="citation journal cs1">Cramer, John; Forward, Robert; Morris, Michael; Visser, Matt; Benford, Gregory; Landis, Geoffrey (1995). "Natural wormholes as gravitational lenses". <i>Physical Review D</i>. <b>51</b> (6): <span class="nowrap">3117–</span>3120. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/9409051">astro-ph/9409051</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1995PhRvD..51.3117C">1995PhRvD..51.3117C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.51.3117">10.1103/PhysRevD.51.3117</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/10018782">10018782</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:42837620">42837620</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=Natural+wormholes+as+gravitational+lenses&rft.volume=51&rft.issue=6&rft.pages=%3Cspan+class%3D%22nowrap%22%3E3117-%3C%2Fspan%3E3120&rft.date=1995&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A42837620%23id-name%3DS2CID&rft_id=info%3Abibcode%2F1995PhRvD..51.3117C&rft_id=info%3Aarxiv%2Fastro-ph%2F9409051&rft_id=info%3Apmid%2F10018782&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.51.3117&rft.aulast=Cramer&rft.aufirst=John&rft.au=Forward%2C+Robert&rft.au=Morris%2C+Michael&rft.au=Visser%2C+Matt&rft.au=Benford%2C+Gregory&rft.au=Landis%2C+Geoffrey&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation pressrelease cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20120415100921/http://www.geoffreylandis.com/wormholes.htp">"Searching for a 'Subway to the Stars'<span class="cs1-kern-right"></span>"</a> (Press release). Archived from <a rel="nofollow" class="external text" href="http://www.geoffreylandis.com/wormholes.htp">the original</a> on 2012-04-15.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Searching+for+a+%27Subway+to+the+Stars%27&rft_id=http%3A%2F%2Fwww.geoffreylandis.com%2Fwormholes.htp&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFThorne1994" class="citation book cs1">Thorne, Kip S. (1994). <i>Black holes and time warps : Einstein's outrageous legacy</i>. New York. p. 493. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0393312768" title="Special:BookSources/978-0393312768"><bdi>978-0393312768</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Black+holes+and+time+warps+%3A+Einstein%27s+outrageous+legacy&rft.place=New+York&rft.pages=493&rft.date=1994&rft.isbn=978-0393312768&rft.aulast=Thorne&rft.aufirst=Kip+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: location missing publisher (<a href="/wiki/Category:CS1_maint:_location_missing_publisher" title="Category:CS1 maint: location missing publisher">link</a>)</span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeyl1921" class="citation journal cs1">Weyl, H. (1921). <a rel="nofollow" class="external text" href="https://zenodo.org/record/1424373">"Feld und Materie"</a>. <i>Annalen der Physik</i>. <b>65</b> (14): <span class="nowrap">541–</span>563. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1921AnP...370..541W">1921AnP...370..541W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.19213701405">10.1002/andp.19213701405</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik&rft.atitle=Feld+und+Materie&rft.volume=65&rft.issue=14&rft.pages=%3Cspan+class%3D%22nowrap%22%3E541-%3C%2Fspan%3E563&rft.date=1921&rft_id=info%3Adoi%2F10.1002%2Fandp.19213701405&rft_id=info%3Abibcode%2F1921AnP...370..541W&rft.aulast=Weyl&rft.aufirst=H.&rft_id=https%3A%2F%2Fzenodo.org%2Frecord%2F1424373&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFScholz2001" class="citation book cs1">Scholz, Erhard, ed. (2001). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=oZLiqDQGnjgC"><i>Hermann Weyl's Raum – Zeit – Materie and a General Introduction to His Scientific Work</i></a>. Oberwolfach Seminars. Vol. 30. Springer. p. 199. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9783764364762" title="Special:BookSources/9783764364762"><bdi>9783764364762</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Hermann+Weyl%27s+Raum+%E2%80%93+Zeit+%E2%80%93+Materie+and+a+General+Introduction+to+His+Scientific+Work&rft.series=Oberwolfach+Seminars&rft.pages=199&rft.pub=Springer&rft.date=2001&rft.isbn=9783764364762&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DoZLiqDQGnjgC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-SEP-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-SEP_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-SEP_9-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://plato.stanford.edu/entries/weyl/">"Hermann Weyl"</a>: entry in the <i><a href="/wiki/Stanford_Encyclopedia_of_Philosophy" title="Stanford Encyclopedia of Philosophy">Stanford Encyclopedia of Philosophy</a></i>.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBlum2022" class="citation journal cs1">Blum, Alexander S. (2022). <a rel="nofollow" class="external text" href="https://onlinelibrary.wiley.com/doi/10.1002/andp.202200244">"From Wood Chuck Holes to Worm Holes—A Look into the Notebooks of John A. Wheeler"</a>. <i>Annalen der Physik</i>. <b>534</b> (8): 2200244. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.202200244">10.1002/andp.202200244</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1521-3889">1521-3889</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik&rft.atitle=From+Wood+Chuck+Holes+to+Worm+Holes%E2%80%94A+Look+into+the+Notebooks+of+John+A.+Wheeler&rft.volume=534&rft.issue=8&rft.pages=2200244&rft.date=2022&rft_id=info%3Adoi%2F10.1002%2Fandp.202200244&rft.issn=1521-3889&rft.aulast=Blum&rft.aufirst=Alexander+S.&rft_id=https%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1002%2Fandp.202200244&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMisnerThorneZurek2009" class="citation journal cs1">Misner, Charles W.; Thorne, Kip S.; Zurek, Wojciech H. (2009-04-01). <a rel="nofollow" class="external text" href="https://pubs.aip.org/physicstoday/article-abstract/62/4/40/390982/John-Wheeler-relativity-and-quantum?redirectedFrom=fulltext">"John Wheeler, relativity, and quantum information"</a>. <i>Physics Today</i>. <b>62</b> (4): <span class="nowrap">40–</span>46. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.3120895">10.1063/1.3120895</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0031-9228">0031-9228</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Today&rft.atitle=John+Wheeler%2C+relativity%2C+and+quantum+information&rft.volume=62&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E40-%3C%2Fspan%3E46&rft.date=2009-04-01&rft_id=info%3Adoi%2F10.1063%2F1.3120895&rft.issn=0031-9228&rft.aulast=Misner&rft.aufirst=Charles+W.&rft.au=Thorne%2C+Kip+S.&rft.au=Zurek%2C+Wojciech+H.&rft_id=https%3A%2F%2Fpubs.aip.org%2Fphysicstoday%2Farticle-abstract%2F62%2F4%2F40%2F390982%2FJohn-Wheeler-relativity-and-quantum%3FredirectedFrom%3Dfulltext&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMisnerWheeler1957" class="citation journal cs1">Misner, C. W.; Wheeler, J. A. (1957). "Classical physics as geometry". <i>Ann. Phys</i>. <b>2</b> (6): 525. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1957AnPhy...2..525M">1957AnPhy...2..525M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0003-4916%2857%2990049-0">10.1016/0003-4916(57)90049-0</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Ann.+Phys.&rft.atitle=Classical+physics+as+geometry&rft.volume=2&rft.issue=6&rft.pages=525&rft.date=1957&rft_id=info%3Adoi%2F10.1016%2F0003-4916%2857%2990049-0&rft_id=info%3Abibcode%2F1957AnPhy...2..525M&rft.aulast=Misner&rft.aufirst=C.+W.&rft.au=Wheeler%2C+J.+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-Visser1996-13"><span class="mw-cite-backlink">^ <a href="#cite_ref-Visser1996_13-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Visser1996_13-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVisser1996" class="citation book cs1"><a href="/wiki/Matt_Visser" title="Matt Visser">Visser, Matt</a> (1996). <i>Lorentzian Wormholes</i>. Springer-Verlag. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-56396-653-8" title="Special:BookSources/978-1-56396-653-8"><bdi>978-1-56396-653-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Lorentzian+Wormholes&rft.pub=Springer-Verlag&rft.date=1996&rft.isbn=978-1-56396-653-8&rft.aulast=Visser&rft.aufirst=Matt&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-Rodrigo2-14"><span class="mw-cite-backlink">^ <a href="#cite_ref-Rodrigo2_14-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Rodrigo2_14-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRodrigo2010" class="citation book cs1">Rodrigo, Enrico (2010). <i>The Physics of Stargates</i>. Eridanus Press. p. 281. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-9841500-0-7" title="Special:BookSources/978-0-9841500-0-7"><bdi>978-0-9841500-0-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Physics+of+Stargates&rft.pages=281&rft.pub=Eridanus+Press&rft.date=2010&rft.isbn=978-0-9841500-0-7&rft.aulast=Rodrigo&rft.aufirst=Enrico&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://phys.org/news/2021-03-microscopic-wormholes-theory.html">"Microscopic wormholes possible in theory"</a>. <i>phys.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">22 April</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=phys.org&rft.atitle=Microscopic+wormholes+possible+in+theory&rft_id=https%3A%2F%2Fphys.org%2Fnews%2F2021-03-microscopic-wormholes-theory.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBlázquez-SalcedoKnollRadu2021" class="citation journal cs1">Blázquez-Salcedo, Jose Luis; Knoll, Christian; Radu, Eugen (9 March 2021). <a rel="nofollow" class="external text" href="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.101102">"Traversable Wormholes in Einstein-Dirac-Maxwell Theory"</a>. <i>Physical Review Letters</i>. <b>126</b> (10): 101102. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/2010.07317">2010.07317</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2021PhRvL.126j1102B">2021PhRvL.126j1102B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.126.101102">10.1103/PhysRevLett.126.101102</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/10773%2F32560">10773/32560</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/33784127">33784127</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:222378921">222378921</a><span class="reference-accessdate">. Retrieved <span class="nowrap">22 April</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Traversable+Wormholes+in+Einstein-Dirac-Maxwell+Theory&rft.volume=126&rft.issue=10&rft.pages=101102&rft.date=2021-03-09&rft_id=info%3Ahdl%2F10773%2F32560&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A222378921%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2021PhRvL.126j1102B&rft_id=info%3Aarxiv%2F2010.07317&rft_id=info%3Apmid%2F33784127&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.126.101102&rft.aulast=Bl%C3%A1zquez-Salcedo&rft.aufirst=Jose+Luis&rft.au=Knoll%2C+Christian&rft.au=Radu%2C+Eugen&rft_id=https%3A%2F%2Fjournals.aps.org%2Fprl%2Fabstract%2F10.1103%2FPhysRevLett.126.101102&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKonoplyaZhidenko2022" class="citation journal cs1">Konoplya, R. A.; Zhidenko, A. (4 March 2022). <a rel="nofollow" class="external text" href="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.091104">"Traversable Wormholes in General Relativity"</a>. <i>Physical Review Letters</i>. <b>128</b> (9): 091104. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/2106.05034">2106.05034</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2022PhRvL.128i1104K">2022PhRvL.128i1104K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.128.091104">10.1103/PhysRevLett.128.091104</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/35302821">35302821</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:247245028">247245028</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Traversable+Wormholes+in+General+Relativity&rft.volume=128&rft.issue=9&rft.pages=091104&rft.date=2022-03-04&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A247245028%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2022PhRvL.128i1104K&rft_id=info%3Aarxiv%2F2106.05034&rft_id=info%3Apmid%2F35302821&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.128.091104&rft.aulast=Konoplya&rft.aufirst=R.+A.&rft.au=Zhidenko%2C+A.&rft_id=https%3A%2F%2Fjournals.aps.org%2Fprl%2Fabstract%2F10.1103%2FPhysRevLett.128.091104&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchirber2021" class="citation news cs1">Schirber, Michael (9 March 2021). <a rel="nofollow" class="external text" href="https://physics.aps.org/articles/v14/s28">"Wormholes Open for Transport"</a>. <i>Physics</i><span class="reference-accessdate">. Retrieved <span class="nowrap">22 April</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics&rft.atitle=Wormholes+Open+for+Transport&rft.date=2021-03-09&rft.aulast=Schirber&rft.aufirst=Michael&rft_id=https%3A%2F%2Fphysics.aps.org%2Farticles%2Fv14%2Fs28&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMaldacenaMilekhin2021" class="citation journal cs1">Maldacena, Juan; Milekhin, Alexey (9 March 2021). <a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.103.066007">"Humanly traversable wormholes"</a>. <i>Physical Review D</i>. <b>103</b> (6): 066007. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/2008.06618">2008.06618</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2021PhRvD.103f6007M">2021PhRvD.103f6007M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.103.066007">10.1103/PhysRevD.103.066007</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=Humanly+traversable+wormholes&rft.volume=103&rft.issue=6&rft.pages=066007&rft.date=2021-03-09&rft_id=info%3Aarxiv%2F2008.06618&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.103.066007&rft_id=info%3Abibcode%2F2021PhRvD.103f6007M&rft.aulast=Maldacena&rft.aufirst=Juan&rft.au=Milekhin%2C+Alexey&rft_id=https%3A%2F%2Fdoi.org%2F10.1103%252FPhysRevD.103.066007&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span> <span typeof="mw:File"><a href="/wiki/File:CC_BY_icon.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e1/CC_BY_icon.svg/50px-CC_BY_icon.svg.png" decoding="async" width="50" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e1/CC_BY_icon.svg/75px-CC_BY_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e1/CC_BY_icon.svg/100px-CC_BY_icon.svg.png 2x" data-file-width="88" data-file-height="31" /></a></span> Available under <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by/4.0/">CC BY 4.0</a>.</span> </li> <li id="cite_note-Dobrev-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-Dobrev_20-0">^</a></b></span> <span class="reference-text">Vladimir Dobrev (ed.), <i>Lie Theory and Its Applications in Physics: Varna, Bulgaria, June 2015</i>, Springer, 2016, p. 246.</span> </li> <li id="cite_note-ER-21"><span class="mw-cite-backlink">^ <a href="#cite_ref-ER_21-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-ER_21-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">A. Einstein and N. Rosen, "The Particle Problem in the General Theory of Relativity," <i>Phys. Rev.</i> <b>48</b>(73) (1935).</span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=9P6rdqiybaw">"Black Holes Explained – From Birth to Death"</a>. <i><a href="/wiki/YouTube" title="YouTube">YouTube</a></i>. 12 August 2018. <a rel="nofollow" class="external text" href="https://ghostarchive.org/varchive/youtube/20211211/9P6rdqiybaw">Archived</a> from the original on 2021-12-11.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=YouTube&rft.atitle=Black+Holes+Explained+%E2%80%93+From+Birth+to+Death&rft.date=2018-08-12&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D9P6rdqiybaw&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://casa.colorado.edu/~ajsh/collapse.html#kruskal">"Collapse to a Black Hole"</a>. Casa.colorado.edu. 2010-10-03<span class="reference-accessdate">. Retrieved <span class="nowrap">2010-11-11</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Collapse+to+a+Black+Hole&rft.pub=Casa.colorado.edu&rft.date=2010-10-03&rft_id=http%3A%2F%2Fcasa.colorado.edu%2F~ajsh%2Fcollapse.html%23kruskal&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span> <small>This <a href="/wiki/Wikipedia:Tertiary_sources" class="mw-redirect" title="Wikipedia:Tertiary sources">tertiary source</a> reuses information from other sources but does not name them.</small></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFlamm1916" class="citation journal cs1">Flamm (1916). "Beiträge zur Einsteinschen Gravitationstheorie". <i><a href="/wiki/Physikalische_Zeitschrift" title="Physikalische Zeitschrift">Physikalische Zeitschrift</a></i>. <b>XVII</b>: 448.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physikalische+Zeitschrift&rft.atitle=Beitr%C3%A4ge+zur+Einsteinschen+Gravitationstheorie&rft.volume=XVII&rft.pages=448&rft.date=1916&rft.au=Flamm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span> ("Comments on Einstein's Theory of Gravity")</span> </li> <li id="cite_note-focus032505-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-focus032505_25-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLindley2005" class="citation journal cs1">Lindley, David (Mar 25, 2005). <a rel="nofollow" class="external text" href="http://physics.aps.org/story/v15/st11">"Focus: The Birth of Wormholes"</a>. <i>Physics</i>. <b>15</b>. American Physical Society<span class="reference-accessdate">. Retrieved <span class="nowrap">20 February</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics&rft.atitle=Focus%3A+The+Birth+of+Wormholes&rft.volume=15&rft.date=2005-03-25&rft.aulast=Lindley&rft.aufirst=David&rft_id=http%3A%2F%2Fphysics.aps.org%2Fstory%2Fv15%2Fst11&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFullerWheeler1962" class="citation journal cs1">Fuller, Robert W.; Wheeler, John A. (1962-10-15). "Causality and Multiply Connected Space-Time". <i>Physical Review</i>. <b>128</b> (2). American Physical Society (APS): <span class="nowrap">919–</span>929. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1962PhRv..128..919F">1962PhRv..128..919F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2Fphysrev.128.919">10.1103/physrev.128.919</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0031-899X">0031-899X</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review&rft.atitle=Causality+and+Multiply+Connected+Space-Time&rft.volume=128&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E919-%3C%2Fspan%3E929&rft.date=1962-10-15&rft.issn=0031-899X&rft_id=info%3Adoi%2F10.1103%2Fphysrev.128.919&rft_id=info%3Abibcode%2F1962PhRv..128..919F&rft.aulast=Fuller&rft.aufirst=Robert+W.&rft.au=Wheeler%2C+John+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoplawski,_Nikodem_J.2010" class="citation journal cs1"><a href="/wiki/Nikodem_Pop%C5%82awski" title="Nikodem Popławski">Poplawski, Nikodem J.</a> (2010). "Cosmology with torsion: An alternative to cosmic inflation". <i>Phys. Lett. B</i>. <b>694</b> (3): <span class="nowrap">181–</span>185. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1007.0587">1007.0587</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2010PhLB..694..181P">2010PhLB..694..181P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.physletb.2010.09.056">10.1016/j.physletb.2010.09.056</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Phys.+Lett.+B&rft.atitle=Cosmology+with+torsion%3A+An+alternative+to+cosmic+inflation&rft.volume=694&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E181-%3C%2Fspan%3E185&rft.date=2010&rft_id=info%3Aarxiv%2F1007.0587&rft_id=info%3Adoi%2F10.1016%2Fj.physletb.2010.09.056&rft_id=info%3Abibcode%2F2010PhLB..694..181P&rft.au=Poplawski%2C+Nikodem+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFThorne1994" class="citation book cs1">Thorne, Kip S. (1994). <i>Black holes and time warps : Einstein's outrageous legacy</i>. New York. p. 488. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0393312768" title="Special:BookSources/978-0393312768"><bdi>978-0393312768</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Black+holes+and+time+warps+%3A+Einstein%27s+outrageous+legacy&rft.place=New+York&rft.pages=488&rft.date=1994&rft.isbn=978-0393312768&rft.aulast=Thorne&rft.aufirst=Kip+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: location missing publisher (<a href="/wiki/Category:CS1_maint:_location_missing_publisher" title="Category:CS1 maint: location missing publisher">link</a>)</span></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJ._Wheeler1957" class="citation journal cs1">J. Wheeler (1957). "On the nature of quantum geometrodynamics". <i>Ann. Phys</i>. <b>2</b> (6): <span class="nowrap">604–</span>614. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1957AnPhy...2..604W">1957AnPhy...2..604W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0003-4916%2857%2990050-7">10.1016/0003-4916(57)90050-7</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Ann.+Phys.&rft.atitle=On+the+nature+of+quantum+geometrodynamics&rft.volume=2&rft.issue=6&rft.pages=%3Cspan+class%3D%22nowrap%22%3E604-%3C%2Fspan%3E614&rft.date=1957&rft_id=info%3Adoi%2F10.1016%2F0003-4916%2857%2990050-7&rft_id=info%3Abibcode%2F1957AnPhy...2..604W&rft.au=J.+Wheeler&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span> (A follow-up paper to Misner and Wheeler (December 1957).)</span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text">Eduard Prugovecki, <i>Quantum Geometry: A Framework for Quantum General Relativity</i>, Springer, 2013, p. 412.</span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEverettRoman2012" class="citation book cs1">Everett, Allen; Roman, Thomas (2012). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/isbn_9780226224985"><i>Time Travel and Warp Drives</i></a></span>. <a href="/wiki/University_of_Chicago_Press" title="University of Chicago Press">University of Chicago Press</a>. p. <a rel="nofollow" class="external text" href="https://archive.org/details/isbn_9780226224985/page/n182">167</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-226-22498-5" title="Special:BookSources/978-0-226-22498-5"><bdi>978-0-226-22498-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Time+Travel+and+Warp+Drives&rft.pages=167&rft.pub=University+of+Chicago+Press&rft.date=2012&rft.isbn=978-0-226-22498-5&rft.aulast=Everett&rft.aufirst=Allen&rft.au=Roman%2C+Thomas&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fisbn_9780226224985&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-32">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20120210233225/http://www.hawking.org.uk/space-and-time-warps.html">"Space and Time Warps"</a>. <i>Hawking.org.uk</i>. Archived from <a rel="nofollow" class="external text" href="http://www.hawking.org.uk/space-and-time-warps.html">the original</a> on 2012-02-10<span class="reference-accessdate">. Retrieved <span class="nowrap">2010-11-11</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Hawking.org.uk&rft.atitle=Space+and+Time+Warps&rft_id=http%3A%2F%2Fwww.hawking.org.uk%2Fspace-and-time-warps.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-time_travel-33"><span class="mw-cite-backlink">^ <a href="#cite_ref-time_travel_33-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-time_travel_33-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-time_travel_33-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMorrisThorneYurtsever1988" class="citation journal cs1">Morris, Michael; Thorne, Kip; Yurtsever, Ulvi (1988). <a rel="nofollow" class="external text" href="http://authors.library.caltech.edu/9262/1/MORprl88.pdf">"Wormholes, Time Machines, and the Weak Energy Condition"</a> <span class="cs1-format">(PDF)</span>. <i>Physical Review Letters</i>. <b>61</b> (13): <span class="nowrap">1446–</span>1449. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1988PhRvL..61.1446M">1988PhRvL..61.1446M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.61.1446">10.1103/PhysRevLett.61.1446</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/10038800">10038800</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Wormholes%2C+Time+Machines%2C+and+the+Weak+Energy+Condition&rft.volume=61&rft.issue=13&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1446-%3C%2Fspan%3E1449&rft.date=1988&rft_id=info%3Apmid%2F10038800&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.61.1446&rft_id=info%3Abibcode%2F1988PhRvL..61.1446M&rft.aulast=Morris&rft.aufirst=Michael&rft.au=Thorne%2C+Kip&rft.au=Yurtsever%2C+Ulvi&rft_id=http%3A%2F%2Fauthors.library.caltech.edu%2F9262%2F1%2FMORprl88.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSopovaFord2002" class="citation journal cs1">Sopova; Ford (2002). "The Energy Density in the Casimir Effect". <i><a href="/wiki/Physical_Review_D" class="mw-redirect" title="Physical Review D">Physical Review D</a></i>. <b>66</b> (4): 045026. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/quant-ph/0204125">quant-ph/0204125</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2002PhRvD..66d5026S">2002PhRvD..66d5026S</a>. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.251.7471">10.1.1.251.7471</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.66.045026">10.1103/PhysRevD.66.045026</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:10649139">10649139</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=The+Energy+Density+in+the+Casimir+Effect&rft.volume=66&rft.issue=4&rft.pages=045026&rft.date=2002&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A10649139%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2002PhRvD..66d5026S&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.251.7471%23id-name%3DCiteSeerX&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.66.045026&rft_id=info%3Aarxiv%2Fquant-ph%2F0204125&rft.au=Sopova&rft.au=Ford&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFordRoman1995" class="citation journal cs1">Ford; Roman (1995). "Averaged Energy Conditions and Quantum Inequalities". <i><a href="/wiki/Physical_Review_D" class="mw-redirect" title="Physical Review D">Physical Review D</a></i>. <b>51</b> (8): <span class="nowrap">4277–</span>4286. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/9410043">gr-qc/9410043</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1995PhRvD..51.4277F">1995PhRvD..51.4277F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.51.4277">10.1103/PhysRevD.51.4277</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/10018903">10018903</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:7413835">7413835</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=Averaged+Energy+Conditions+and+Quantum+Inequalities&rft.volume=51&rft.issue=8&rft.pages=%3Cspan+class%3D%22nowrap%22%3E4277-%3C%2Fspan%3E4286&rft.date=1995&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A7413835%23id-name%3DS2CID&rft_id=info%3Abibcode%2F1995PhRvD..51.4277F&rft_id=info%3Aarxiv%2Fgr-qc%2F9410043&rft_id=info%3Apmid%2F10018903&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.51.4277&rft.au=Ford&rft.au=Roman&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOlum1998" class="citation journal cs1">Olum (1998). "Superluminal travel requires negative energies". <i><a href="/wiki/Physical_Review_Letters" title="Physical Review Letters">Physical Review Letters</a></i>. <b>81</b> (17): <span class="nowrap">3567–</span>3570. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/9805003">gr-qc/9805003</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1998PhRvL..81.3567O">1998PhRvL..81.3567O</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.81.3567">10.1103/PhysRevLett.81.3567</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:14513456">14513456</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Superluminal+travel+requires+negative+energies&rft.volume=81&rft.issue=17&rft.pages=%3Cspan+class%3D%22nowrap%22%3E3567-%3C%2Fspan%3E3570&rft.date=1998&rft_id=info%3Aarxiv%2Fgr-qc%2F9805003&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A14513456%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.81.3567&rft_id=info%3Abibcode%2F1998PhRvL..81.3567O&rft.au=Olum&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-37">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.quantamagazine.org/newfound-wormhole-allows-information-to-escape-black-holes-20171023/">"Newfound Wormhole Allows Information to Escape Black Holes"</a>. <i>Quanta Magazine</i>. 23 October 2017.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Quanta+Magazine&rft.atitle=Newfound+Wormhole+Allows+Information+to+Escape+Black+Holes&rft.date=2017-10-23&rft_id=https%3A%2F%2Fwww.quantamagazine.org%2Fnewfound-wormhole-allows-information-to-escape-black-holes-20171023%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-Thorne1994-38"><span class="mw-cite-backlink">^ <a href="#cite_ref-Thorne1994_38-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Thorne1994_38-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Thorne1994_38-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Thorne1994_38-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFThorne1994" class="citation book cs1"><a href="/wiki/Kip_Thorne" title="Kip Thorne">Thorne, Kip S.</a> (1994). <a href="/wiki/Black_Holes_and_Time_Warps" title="Black Holes and Time Warps"><i>Black Holes and Time Warps</i></a>. W. W. Norton. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-393-31276-8" title="Special:BookSources/978-0-393-31276-8"><bdi>978-0-393-31276-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Black+Holes+and+Time+Warps&rft.pub=W.+W.+Norton&rft.date=1994&rft.isbn=978-0-393-31276-8&rft.aulast=Thorne&rft.aufirst=Kip+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-quantumdynamics-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-quantumdynamics_39-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFIan_H.Wai-Mo_Suen1994" class="citation journal cs1">Ian H., Redmount; Wai-Mo Suen (1994). "Quantum Dynamics of Lorentzian Spacetime Foam". <i><a href="/wiki/Physical_Review_D" class="mw-redirect" title="Physical Review D">Physical Review D</a></i>. <b>49</b> (10): <span class="nowrap">5199–</span>5210. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/9309017">gr-qc/9309017</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1994PhRvD..49.5199R">1994PhRvD..49.5199R</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.49.5199">10.1103/PhysRevD.49.5199</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/10016836">10016836</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:39296197">39296197</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=Quantum+Dynamics+of+Lorentzian+Spacetime+Foam&rft.volume=49&rft.issue=10&rft.pages=%3Cspan+class%3D%22nowrap%22%3E5199-%3C%2Fspan%3E5210&rft.date=1994&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A39296197%23id-name%3DS2CID&rft_id=info%3Abibcode%2F1994PhRvD..49.5199R&rft_id=info%3Aarxiv%2Fgr-qc%2F9309017&rft_id=info%3Apmid%2F10016836&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.49.5199&rft.aulast=Ian+H.&rft.aufirst=Redmount&rft.au=Wai-Mo+Suen&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-40">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKirillovP._Savelova2008" class="citation journal cs1">Kirillov, A. A.; P. Savelova, E. (2008). "Dark Matter from a gas of wormholes". <i><a href="/wiki/Physics_Letters_B" class="mw-redirect" title="Physics Letters B">Physics Letters B</a></i>. <b>660</b> (3): <span class="nowrap">93–</span>99. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/0707.1081">0707.1081</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2008PhLB..660...93K">2008PhLB..660...93K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.physletb.2007.12.034">10.1016/j.physletb.2007.12.034</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:12150385">12150385</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Letters+B&rft.atitle=Dark+Matter+from+a+gas+of+wormholes&rft.volume=660&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E93-%3C%2Fspan%3E99&rft.date=2008&rft_id=info%3Aarxiv%2F0707.1081&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A12150385%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.physletb.2007.12.034&rft_id=info%3Abibcode%2F2008PhLB..660...93K&rft.aulast=Kirillov&rft.aufirst=A.+A.&rft.au=P.+Savelova%2C+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-41">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRodrigo2009" class="citation journal cs1">Rodrigo, Enrico (2009). "Denouement of a Wormhole-Brane Encounter". <i><a href="/wiki/International_Journal_of_Modern_Physics_D" class="mw-redirect" title="International Journal of Modern Physics D">International Journal of Modern Physics D</a></i>. <b>18</b> (12): <span class="nowrap">1809–</span>1819. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/0908.2651">0908.2651</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009IJMPD..18.1809R">2009IJMPD..18.1809R</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1142%2FS0218271809015333">10.1142/S0218271809015333</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:119239038">119239038</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+of+Modern+Physics+D&rft.atitle=Denouement+of+a+Wormhole-Brane+Encounter&rft.volume=18&rft.issue=12&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1809-%3C%2Fspan%3E1819&rft.date=2009&rft_id=info%3Aarxiv%2F0908.2651&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119239038%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1142%2FS0218271809015333&rft_id=info%3Abibcode%2F2009IJMPD..18.1809R&rft.aulast=Rodrigo&rft.aufirst=Enrico&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-naturalwormholes-42"><span class="mw-cite-backlink">^ <a href="#cite_ref-naturalwormholes_42-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-naturalwormholes_42-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJohn_G._CramerRobert_L._ForwardMichael_S._MorrisMatt_Visser1995" class="citation journal cs1">John G. Cramer; Robert L. Forward; Michael S. Morris; Matt Visser; Gregory Benford & Geoffrey A. Landis (1995). <a rel="nofollow" class="external text" href="https://cds.cern.ch/record/268926">"Natural Wormholes as Gravitational Lenses"</a>. <i><a href="/wiki/Physical_Review_D" class="mw-redirect" title="Physical Review D">Physical Review D</a></i>. <b>51</b> (6): <span class="nowrap">3117–</span>3120. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/9409051">astro-ph/9409051</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1995PhRvD..51.3117C">1995PhRvD..51.3117C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.51.3117">10.1103/PhysRevD.51.3117</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/10018782">10018782</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:42837620">42837620</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=Natural+Wormholes+as+Gravitational+Lenses&rft.volume=51&rft.issue=6&rft.pages=%3Cspan+class%3D%22nowrap%22%3E3117-%3C%2Fspan%3E3120&rft.date=1995&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A42837620%23id-name%3DS2CID&rft_id=info%3Abibcode%2F1995PhRvD..51.3117C&rft_id=info%3Aarxiv%2Fastro-ph%2F9409051&rft_id=info%3Apmid%2F10018782&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.51.3117&rft.au=John+G.+Cramer&rft.au=Robert+L.+Forward&rft.au=Michael+S.+Morris&rft.au=Matt+Visser&rft.au=Gregory+Benford&rft.au=Geoffrey+A.+Landis&rft_id=https%3A%2F%2Fcds.cern.ch%2Frecord%2F268926&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-ellis1-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-ellis1_44-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFH._G._Ellis1973" class="citation journal cs1">H. G. Ellis (1973). "Ether flow through a drainhole: A particle model in general relativity". <i>Journal of Mathematical Physics</i>. <b>14</b> (1): <span class="nowrap">104–</span>118. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1973JMP....14..104E">1973JMP....14..104E</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.1666161">10.1063/1.1666161</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Mathematical+Physics&rft.atitle=Ether+flow+through+a+drainhole%3A+A+particle+model+in+general+relativity&rft.volume=14&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E104-%3C%2Fspan%3E118&rft.date=1973&rft_id=info%3Adoi%2F10.1063%2F1.1666161&rft_id=info%3Abibcode%2F1973JMP....14..104E&rft.au=H.+G.+Ellis&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-bron-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-bron_45-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFK._A._Bronnikov1973" class="citation journal cs1">K. A. Bronnikov (1973). "Scalar-tensor theory and scalar charge". <i>Acta Physica Polonica</i>. <b>B4</b>: <span class="nowrap">251–</span>266.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Acta+Physica+Polonica&rft.atitle=Scalar-tensor+theory+and+scalar+charge&rft.volume=B4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E251-%3C%2Fspan%3E266&rft.date=1973&rft.au=K.+A.+Bronnikov&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-46">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMorris,_Michael_S.Thorne,_Kip_S.1988" class="citation journal cs1">Morris, Michael S. & Thorne, Kip S. (1988). <a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.15620">"Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity"</a>. <i><a href="/wiki/American_Journal_of_Physics" title="American Journal of Physics">American Journal of Physics</a></i>. <b>56</b> (5): <span class="nowrap">395–</span>412. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1988AmJPh..56..395M">1988AmJPh..56..395M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.15620">10.1119/1.15620</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=Wormholes+in+spacetime+and+their+use+for+interstellar+travel%3A+A+tool+for+teaching+general+relativity&rft.volume=56&rft.issue=5&rft.pages=%3Cspan+class%3D%22nowrap%22%3E395-%3C%2Fspan%3E412&rft.date=1988&rft_id=info%3Adoi%2F10.1119%2F1.15620&rft_id=info%3Abibcode%2F1988AmJPh..56..395M&rft.au=Morris%2C+Michael+S.&rft.au=Thorne%2C+Kip+S.&rft_id=https%3A%2F%2Fdoi.org%2F10.1119%252F1.15620&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-47"><span class="mw-cite-backlink"><b><a href="#cite_ref-47">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFElias_GravanisSteven_Willison2007" class="citation journal cs1">Elias Gravanis; Steven Willison (2007). "<span class="cs1-kern-left"></span>'Mass without mass' from thin shells in Gauss-Bonnet gravity". <i>Phys. Rev. D</i>. <b>75</b> (8): 084025. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/0701152">gr-qc/0701152</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2007PhRvD..75h4025G">2007PhRvD..75h4025G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.75.084025">10.1103/PhysRevD.75.084025</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:53529713">53529713</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Phys.+Rev.+D&rft.atitle=%27Mass+without+mass%27+from+thin+shells+in+Gauss-Bonnet+gravity&rft.volume=75&rft.issue=8&rft.pages=084025&rft.date=2007&rft_id=info%3Aarxiv%2Fgr-qc%2F0701152&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A53529713%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.75.084025&rft_id=info%3Abibcode%2F2007PhRvD..75h4025G&rft.au=Elias+Gravanis&rft.au=Steven+Willison&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-48"><span class="mw-cite-backlink"><b><a href="#cite_ref-48">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFewsterKen_D._OlumMichael_J._Pfenning2007" class="citation journal cs1">Fewster, Christopher J.; Ken D. Olum; Michael J. Pfenning (2007). "Averaged null energy condition in spacetimes with boundaries". <i>Physical Review D</i>. <b>75</b> (2): 025007. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/0609007">gr-qc/0609007</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2007PhRvD..75b5007F">2007PhRvD..75b5007F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.75.025007">10.1103/PhysRevD.75.025007</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:119726654">119726654</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=Averaged+null+energy+condition+in+spacetimes+with+boundaries&rft.volume=75&rft.issue=2&rft.pages=025007&rft.date=2007&rft_id=info%3Aarxiv%2Fgr-qc%2F0609007&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119726654%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.75.025007&rft_id=info%3Abibcode%2F2007PhRvD..75b5007F&rft.aulast=Fewster&rft.aufirst=Christopher+J.&rft.au=Ken+D.+Olum&rft.au=Michael+J.+Pfenning&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-49"><span class="mw-cite-backlink"><b><a href="#cite_ref-49">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVisser1996" class="citation journal cs1">Visser, Matt (1996). "Gravitational vacuum polarization. II. Energy conditions in the Boulware vacuum". <i>Physical Review D</i>. <b>54</b> (8): <span class="nowrap">5116–</span>5122. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/9604008">gr-qc/9604008</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1996PhRvD..54.5116V">1996PhRvD..54.5116V</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.54.5116">10.1103/PhysRevD.54.5116</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/10021199">10021199</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:31954680">31954680</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=Gravitational+vacuum+polarization.+II.+Energy+conditions+in+the+Boulware+vacuum&rft.volume=54&rft.issue=8&rft.pages=%3Cspan+class%3D%22nowrap%22%3E5116-%3C%2Fspan%3E5122&rft.date=1996&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A31954680%23id-name%3DS2CID&rft_id=info%3Abibcode%2F1996PhRvD..54.5116V&rft_id=info%3Aarxiv%2Fgr-qc%2F9604008&rft_id=info%3Apmid%2F10021199&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.54.5116&rft.aulast=Visser&rft.aufirst=Matt&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-50"><span class="mw-cite-backlink"><b><a href="#cite_ref-50">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrahamKen_D._Olum2007" class="citation journal cs1">Graham, Noah; Ken D. Olum (2007). "Achronal averaged null energy condition". <i>Physical Review D</i>. <b>76</b> (6): 064001. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/0705.3193">0705.3193</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2007PhRvD..76f4001G">2007PhRvD..76f4001G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.76.064001">10.1103/PhysRevD.76.064001</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:119285639">119285639</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=Achronal+averaged+null+energy+condition&rft.volume=76&rft.issue=6&rft.pages=064001&rft.date=2007&rft_id=info%3Aarxiv%2F0705.3193&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119285639%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.76.064001&rft_id=info%3Abibcode%2F2007PhRvD..76f4001G&rft.aulast=Graham&rft.aufirst=Noah&rft.au=Ken+D.+Olum&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-51"><span class="mw-cite-backlink"><b><a href="#cite_ref-51">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFUrbanKen_D._Olum2010" class="citation journal cs1">Urban, Douglas; Ken D. Olum (2010). "Spacetime averaged null energy condition". <i>Physical Review D</i>. <b>81</b> (6): 124004. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1002.4689">1002.4689</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2010PhRvD..81l4004U">2010PhRvD..81l4004U</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.81.124004">10.1103/PhysRevD.81.124004</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:118312373">118312373</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=Spacetime+averaged+null+energy+condition&rft.volume=81&rft.issue=6&rft.pages=124004&rft.date=2010&rft_id=info%3Aarxiv%2F1002.4689&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A118312373%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.81.124004&rft_id=info%3Abibcode%2F2010PhRvD..81l4004U&rft.aulast=Urban&rft.aufirst=Douglas&rft.au=Ken+D.+Olum&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-52"><span class="mw-cite-backlink"><b><a href="#cite_ref-52">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDuplessisEasson2015" class="citation journal cs1">Duplessis, Francis; Easson, Damien A. (2015). "Exotica ex nihilo: Traversable wormholes & non-singular black holes from the vacuum of quadratic gravity". <i>Physical Review D</i>. <b>92</b> (4): 043516. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1506.00988">1506.00988</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2015PhRvD..92d3516D">2015PhRvD..92d3516D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.92.043516">10.1103/PhysRevD.92.043516</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:118307327">118307327</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=Exotica+ex+nihilo%3A+Traversable+wormholes+%26+non-singular+black+holes+from+the+vacuum+of+quadratic+gravity&rft.volume=92&rft.issue=4&rft.pages=043516&rft.date=2015&rft_id=info%3Aarxiv%2F1506.00988&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A118307327%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.92.043516&rft_id=info%3Abibcode%2F2015PhRvD..92d3516D&rft.aulast=Duplessis&rft.aufirst=Francis&rft.au=Easson%2C+Damien+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-53"><span class="mw-cite-backlink"><b><a href="#cite_ref-53">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSusskind2005" class="citation arxiv cs1">Susskind, Leonard (2005). "Wormholes and Time Travel? Not Likely". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/0503097">gr-qc/0503097</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=Wormholes+and+Time+Travel%3F+Not+Likely&rft.date=2005&rft_id=info%3Aarxiv%2Fgr-qc%2F0503097&rft.aulast=Susskind&rft.aufirst=Leonard&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-54"><span class="mw-cite-backlink"><b><a href="#cite_ref-54">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEverettRoman,_Thomas2012" class="citation book cs1">Everett, Allen; Roman, Thomas (2012). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/isbn_9780226224985"><i>Time Travel and Warp Drives</i></a></span>. University of Chicago Press. p. <a rel="nofollow" class="external text" href="https://archive.org/details/isbn_9780226224985/page/n150">135</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-226-22498-5" title="Special:BookSources/978-0-226-22498-5"><bdi>978-0-226-22498-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Time+Travel+and+Warp+Drives&rft.pages=135&rft.pub=University+of+Chicago+Press&rft.date=2012&rft.isbn=978-0-226-22498-5&rft.aulast=Everett&rft.aufirst=Allen&rft.au=Roman%2C+Thomas&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fisbn_9780226224985&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-casimir-55"><span class="mw-cite-backlink"><b><a href="#cite_ref-casimir_55-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCramer1994" class="citation web cs1"><a href="/wiki/John_G._Cramer" title="John G. Cramer">Cramer, John G.</a> (1994). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060627211046/http://www.npl.washington.edu/av/altvw69.html">"NASA Goes FTL Part 1: Wormhole Physics"</a>. <i>Analog Science Fiction & Fact Magazine</i>. Archived from <a rel="nofollow" class="external text" href="http://www.npl.washington.edu/av/altvw69.html">the original</a> on June 27, 2006<span class="reference-accessdate">. Retrieved <span class="nowrap">December 2,</span> 2006</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Analog+Science+Fiction+%26+Fact+Magazine&rft.atitle=NASA+Goes+FTL+Part+1%3A+Wormhole+Physics&rft.date=1994&rft.aulast=Cramer&rft.aufirst=John+G.&rft_id=http%3A%2F%2Fwww.npl.washington.edu%2Fav%2Faltvw69.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-negative_energy-56"><span class="mw-cite-backlink"><b><a href="#cite_ref-negative_energy_56-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVisserSayan_KarNaresh_Dadhich2003" class="citation journal cs1"><a href="/wiki/Matt_Visser" title="Matt Visser">Visser, Matt</a>; Sayan Kar; Naresh Dadhich (2003). <a rel="nofollow" class="external text" href="https://cds.cern.ch/record/598932">"Traversable wormholes with arbitrarily small energy condition violations"</a>. <i><a href="/wiki/Physical_Review_Letters" title="Physical Review Letters">Physical Review Letters</a></i>. <b>90</b> (20): <span class="nowrap">201102.1 –</span> <span class="nowrap">201102.4</span>. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/0301003">gr-qc/0301003</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2003PhRvL..90t1102V">2003PhRvL..90t1102V</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.90.201102">10.1103/PhysRevLett.90.201102</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/12785880">12785880</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:8813962">8813962</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Traversable+wormholes+with+arbitrarily+small+energy+condition+violations&rft.volume=90&rft.issue=20&rft.pages=%3Cspan+class%3D%22nowrap%22%3E201102.1+-%3C%2Fspan%3E+%3Cspan+class%3D%22nowrap%22%3E201102.4%3C%2Fspan%3E&rft.date=2003&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A8813962%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2003PhRvL..90t1102V&rft_id=info%3Aarxiv%2Fgr-qc%2F0301003&rft_id=info%3Apmid%2F12785880&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.90.201102&rft.aulast=Visser&rft.aufirst=Matt&rft.au=Sayan+Kar&rft.au=Naresh+Dadhich&rft_id=https%3A%2F%2Fcds.cern.ch%2Frecord%2F598932&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-visser_1-57"><span class="mw-cite-backlink"><b><a href="#cite_ref-visser_1_57-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVisser1993" class="citation journal cs1"><a href="/wiki/Matt_Visser" title="Matt Visser">Visser, Matt</a> (1993). "From wormhole to time machine: Comments on Hawking's Chronology Protection Conjecture". <i>Physical Review D</i>. <b>47</b> (2): <span class="nowrap">554–</span>565. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/hep-th/9202090">hep-th/9202090</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1993PhRvD..47..554V">1993PhRvD..47..554V</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.47.554">10.1103/PhysRevD.47.554</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/10015609">10015609</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:16830951">16830951</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=From+wormhole+to+time+machine%3A+Comments+on+Hawking%27s+Chronology+Protection+Conjecture&rft.volume=47&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E554-%3C%2Fspan%3E565&rft.date=1993&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A16830951%23id-name%3DS2CID&rft_id=info%3Abibcode%2F1993PhRvD..47..554V&rft_id=info%3Aarxiv%2Fhep-th%2F9202090&rft_id=info%3Apmid%2F10015609&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.47.554&rft.aulast=Visser&rft.aufirst=Matt&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-58"><span class="mw-cite-backlink"><b><a href="#cite_ref-58">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVisser2002" class="citation book cs1">Visser, Matt (2002). <a rel="nofollow" class="external text" href="https://archive.org/details/arxiv-gr-qc0204022"><i>The quantum physics of chronology protection</i></a>. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/0204022">gr-qc/0204022</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2003ftpc.book..161V">2003ftpc.book..161V</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+quantum+physics+of+chronology+protection&rft.date=2002&rft_id=info%3Aarxiv%2Fgr-qc%2F0204022&rft_id=info%3Abibcode%2F2003ftpc.book..161V&rft.aulast=Visser&rft.aufirst=Matt&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Farxiv-gr-qc0204022&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-visser_2-59"><span class="mw-cite-backlink"><b><a href="#cite_ref-visser_2_59-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVisser1997" class="citation journal cs1"><a href="/wiki/Matt_Visser" title="Matt Visser">Visser, Matt</a> (1997). "Traversable wormholes: the Roman ring". <i>Physical Review D</i>. <b>55</b> (8): <span class="nowrap">5212–</span>5214. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/9702043">gr-qc/9702043</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1997PhRvD..55.5212V">1997PhRvD..55.5212V</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.55.5212">10.1103/PhysRevD.55.5212</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:2869291">2869291</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=Traversable+wormholes%3A+the+Roman+ring&rft.volume=55&rft.issue=8&rft.pages=%3Cspan+class%3D%22nowrap%22%3E5212-%3C%2Fspan%3E5214&rft.date=1997&rft_id=info%3Aarxiv%2Fgr-qc%2F9702043&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A2869291%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.55.5212&rft_id=info%3Abibcode%2F1997PhRvD..55.5212V&rft.aulast=Visser&rft.aufirst=Matt&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-60"><span class="mw-cite-backlink"><b><a href="#cite_ref-60">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDeutsch1991" class="citation journal cs1">Deutsch, David (1991). "Quantum Mechanics Near Closed Timelike Lines". <i><a href="/wiki/Physical_Review_D" class="mw-redirect" title="Physical Review D">Physical Review D</a></i>. <b>44</b> (10): <span class="nowrap">3197–</span>3217. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1991PhRvD..44.3197D">1991PhRvD..44.3197D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.44.3197">10.1103/PhysRevD.44.3197</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/10013776">10013776</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=Quantum+Mechanics+Near+Closed+Timelike+Lines&rft.volume=44&rft.issue=10&rft.pages=%3Cspan+class%3D%22nowrap%22%3E3197-%3C%2Fspan%3E3217&rft.date=1991&rft_id=info%3Apmid%2F10013776&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.44.3197&rft_id=info%3Abibcode%2F1991PhRvD..44.3197D&rft.aulast=Deutsch&rft.aufirst=David&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-61"><span class="mw-cite-backlink"><b><a href="#cite_ref-61">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBrun2009" class="citation journal cs1">Brun; et al. (2009). "Localized Closed Timelike Curves Can Perfectly Distinguish Quantum States". <i><a href="/wiki/Physical_Review_Letters" title="Physical Review Letters">Physical Review Letters</a></i>. <b>102</b> (21): 210402. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/0811.1209">0811.1209</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009PhRvL.102u0402B">2009PhRvL.102u0402B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.102.210402">10.1103/PhysRevLett.102.210402</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/19519086">19519086</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:35370109">35370109</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Localized+Closed+Timelike+Curves+Can+Perfectly+Distinguish+Quantum+States&rft.volume=102&rft.issue=21&rft.pages=210402&rft.date=2009&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A35370109%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2009PhRvL.102u0402B&rft_id=info%3Aarxiv%2F0811.1209&rft_id=info%3Apmid%2F19519086&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.102.210402&rft.au=Brun&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-62"><span class="mw-cite-backlink"><b><a href="#cite_ref-62">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPatiChakrabartyAgrawal2011" class="citation journal cs1">Pati; Chakrabarty; Agrawal (2011). "Purification of mixed states with closed timelike curve is not possible". <i><a href="/wiki/Physical_Review_A" title="Physical Review A">Physical Review A</a></i>. <b>84</b> (6): 062325. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1003.4221">1003.4221</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2011PhRvA..84f2325P">2011PhRvA..84f2325P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevA.84.062325">10.1103/PhysRevA.84.062325</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:119292717">119292717</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+A&rft.atitle=Purification+of+mixed+states+with+closed+timelike+curve+is+not+possible&rft.volume=84&rft.issue=6&rft.pages=062325&rft.date=2011&rft_id=info%3Aarxiv%2F1003.4221&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119292717%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1103%2FPhysRevA.84.062325&rft_id=info%3Abibcode%2F2011PhRvA..84f2325P&rft.au=Pati&rft.au=Chakrabarty&rft.au=Agrawal&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-63"><span class="mw-cite-backlink"><b><a href="#cite_ref-63">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPolchinski1991" class="citation journal cs1">Polchinski, Joseph (1991). "Weinberg's Nonlinear quantum Mechanics and the Einstein–Podolsky–Rosen Paradox". <i><a href="/wiki/Physical_Review_Letters" title="Physical Review Letters">Physical Review Letters</a></i>. <b>66</b> (4): <span class="nowrap">397–</span>400. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1991PhRvL..66..397P">1991PhRvL..66..397P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.66.397">10.1103/PhysRevLett.66.397</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/10043797">10043797</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Weinberg%27s+Nonlinear+quantum+Mechanics+and+the+Einstein%E2%80%93Podolsky%E2%80%93Rosen+Paradox&rft.volume=66&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E397-%3C%2Fspan%3E400&rft.date=1991&rft_id=info%3Apmid%2F10043797&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.66.397&rft_id=info%3Abibcode%2F1991PhRvL..66..397P&rft.aulast=Polchinski&rft.aufirst=Joseph&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-64"><span class="mw-cite-backlink"><b><a href="#cite_ref-64">^</a></b></span> <span class="reference-text">Enrico Rodrigo, <i>The Physics of Stargates: Parallel Universes, Time Travel, and the Enigma of Wormhole Physics</i>, Eridanus Press, 2010, p. 281.</span> </li> <li id="cite_note-65"><span class="mw-cite-backlink"><b><a href="#cite_ref-65">^</a></b></span> <span class="reference-text">Samuel Walker, <a rel="nofollow" class="external text" href="https://www.newscientist.com/letter/mg23331111-100-14-interuniversal-travel-i-wouldnt-start-from-here/">"Inter-universal travel: I wouldn't start from here</a>, <i><a href="/wiki/New_Scientist" title="New Scientist">New Scientist</a></i> (1 February 2017).</span> </li> <li id="cite_note-66"><span class="mw-cite-backlink"><b><a href="#cite_ref-66">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRaineThomas2009" class="citation book cs1">Raine, Derek; Thomas, Edwin (2009). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://archive.org/details/blackholesintrod00rain"><i>Black Holes: An Introduction</i></a></span> (2nd ed.). Imperial College Press. p. <a rel="nofollow" class="external text" href="https://archive.org/details/blackholesintrod00rain/page/n156">143</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1142%2Fp637">10.1142/p637</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-84816-383-6" title="Special:BookSources/978-1-84816-383-6"><bdi>978-1-84816-383-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Black+Holes%3A+An+Introduction&rft.pages=143&rft.edition=2nd&rft.pub=Imperial+College+Press&rft.date=2009&rft_id=info%3Adoi%2F10.1142%2Fp637&rft.isbn=978-1-84816-383-6&rft.aulast=Raine&rft.aufirst=Derek&rft.au=Thomas%2C+Edwin&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fblackholesintrod00rain&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-67"><span class="mw-cite-backlink"><b><a href="#cite_ref-67">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEinsteinRosen1935" class="citation journal cs1">Einstein, A.; Rosen, N. (1 July 1935). <a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.48.73">"The Particle Problem in the General Theory of Relativity"</a>. <i>Physical Review</i>. <b>48</b> (1): <span class="nowrap">73–</span>77. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1935PhRv...48...73E">1935PhRv...48...73E</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.48.73">10.1103/PhysRev.48.73</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review&rft.atitle=The+Particle+Problem+in+the+General+Theory+of+Relativity&rft.volume=48&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E73-%3C%2Fspan%3E77&rft.date=1935-07-01&rft_id=info%3Adoi%2F10.1103%2FPhysRev.48.73&rft_id=info%3Abibcode%2F1935PhRv...48...73E&rft.aulast=Einstein&rft.aufirst=A.&rft.au=Rosen%2C+N.&rft_id=https%3A%2F%2Fdoi.org%2F10.1103%252FPhysRev.48.73&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-68"><span class="mw-cite-backlink"><b><a href="#cite_ref-68">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=OBPpRqxY8Uw">"Leonard Susskind | "ER = EPR" or "What's Behind the Horizons of Black Holes?"<span class="cs1-kern-right"></span>"</a>. 4 November 2014. <a rel="nofollow" class="external text" href="https://ghostarchive.org/varchive/youtube/20211211/OBPpRqxY8Uw">Archived</a> from the original on 2021-12-11 – via www.youtube.com.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Leonard+Susskind+%26%23124%3B+%22ER+%3D+EPR%22+or+%22What%27s+Behind+the+Horizons+of+Black+Holes%3F%22&rft.date=2014-11-04&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DOBPpRqxY8Uw&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-69"><span class="mw-cite-backlink"><b><a href="#cite_ref-69">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.sciencedaily.com/releases/2015/09/150903081506.htm">"Magnetic 'wormhole' connecting two regions of space created for the first time"</a>. <i>ScienceDaily</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=ScienceDaily&rft.atitle=Magnetic+%27wormhole%27+connecting+two+regions+of+space+created+for+the+first+time&rft_id=https%3A%2F%2Fwww.sciencedaily.com%2Freleases%2F2015%2F09%2F150903081506.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> <li id="cite_note-70"><span class="mw-cite-backlink"><b><a href="#cite_ref-70">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.uab.cat/web/newsroom/news-detail/magnetic-wormhole-created-for-first-time-1345668003610.html?noticiaid=1345689132054">"Magnetic wormhole created for first time"</a>. <i>UAB Barcelona</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=UAB+Barcelona&rft.atitle=Magnetic+wormhole+created+for+first+time&rft_id=http%3A%2F%2Fwww.uab.cat%2Fweb%2Fnewsroom%2Fnews-detail%2Fmagnetic-wormhole-created-for-first-time-1345668003610.html%3Fnoticiaid%3D1345689132054&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="Sources">Sources</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wormhole&action=edit&section=19" title="Edit section: Sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDeBenedictis,_AndrewDas,_A.2001" class="citation journal cs1">DeBenedictis, Andrew & Das, A. (2001). "On a General Class of Wormhole Geometries". <i><a href="/wiki/Classical_and_Quantum_Gravity" title="Classical and Quantum Gravity">Classical and Quantum Gravity</a></i>. <b>18</b> (7): <span class="nowrap">1187–</span>1204. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/0009072">gr-qc/0009072</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2001CQGra..18.1187D">2001CQGra..18.1187D</a>. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.339.8662">10.1.1.339.8662</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0264-9381%2F18%2F7%2F304">10.1088/0264-9381/18/7/304</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:119107035">119107035</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Classical+and+Quantum+Gravity&rft.atitle=On+a+General+Class+of+Wormhole+Geometries&rft.volume=18&rft.issue=7&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1187-%3C%2Fspan%3E1204&rft.date=2001&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119107035%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2001CQGra..18.1187D&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.339.8662%23id-name%3DCiteSeerX&rft_id=info%3Adoi%2F10.1088%2F0264-9381%2F18%2F7%2F304&rft_id=info%3Aarxiv%2Fgr-qc%2F0009072&rft.au=DeBenedictis%2C+Andrew&rft.au=Das%2C+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDzhunushaliev,_Vladimir2002" class="citation journal cs1">Dzhunushaliev, Vladimir (2002). "Strings in the Einstein's paradigm of matter". <i><a href="/wiki/Classical_and_Quantum_Gravity" title="Classical and Quantum Gravity">Classical and Quantum Gravity</a></i>. <b>19</b> (19): <span class="nowrap">4817–</span>4824. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/0205055">gr-qc/0205055</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2002CQGra..19.4817D">2002CQGra..19.4817D</a>. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.339.1518">10.1.1.339.1518</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0264-9381%2F19%2F19%2F302">10.1088/0264-9381/19/19/302</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:976106">976106</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Classical+and+Quantum+Gravity&rft.atitle=Strings+in+the+Einstein%27s+paradigm+of+matter&rft.volume=19&rft.issue=19&rft.pages=%3Cspan+class%3D%22nowrap%22%3E4817-%3C%2Fspan%3E4824&rft.date=2002&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A976106%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2002CQGra..19.4817D&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.339.1518%23id-name%3DCiteSeerX&rft_id=info%3Adoi%2F10.1088%2F0264-9381%2F19%2F19%2F302&rft_id=info%3Aarxiv%2Fgr-qc%2F0205055&rft.au=Dzhunushaliev%2C+Vladimir&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEinstein,_AlbertRosen,_Nathan1935" class="citation journal cs1">Einstein, Albert & Rosen, Nathan (1935). <a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.48.73">"The Particle Problem in the General Theory of Relativity"</a>. <i><a href="/wiki/Physical_Review" title="Physical Review">Physical Review</a></i>. <b>48</b> (1): 73. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1935PhRv...48...73E">1935PhRv...48...73E</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.48.73">10.1103/PhysRev.48.73</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review&rft.atitle=The+Particle+Problem+in+the+General+Theory+of+Relativity&rft.volume=48&rft.issue=1&rft.pages=73&rft.date=1935&rft_id=info%3Adoi%2F10.1103%2FPhysRev.48.73&rft_id=info%3Abibcode%2F1935PhRv...48...73E&rft.au=Einstein%2C+Albert&rft.au=Rosen%2C+Nathan&rft_id=https%3A%2F%2Fdoi.org%2F10.1103%252FPhysRev.48.73&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFuller,_Robert_W.Wheeler,_John_A.1962" class="citation journal cs1">Fuller, Robert W. & Wheeler, John A. (1962). "Causality and Multiply-Connected Space-Time". <i><a href="/wiki/Physical_Review" title="Physical Review">Physical Review</a></i>. <b>128</b> (2): 919. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1962PhRv..128..919F">1962PhRv..128..919F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.128.919">10.1103/PhysRev.128.919</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review&rft.atitle=Causality+and+Multiply-Connected+Space-Time&rft.volume=128&rft.issue=2&rft.pages=919&rft.date=1962&rft_id=info%3Adoi%2F10.1103%2FPhysRev.128.919&rft_id=info%3Abibcode%2F1962PhRv..128..919F&rft.au=Fuller%2C+Robert+W.&rft.au=Wheeler%2C+John+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGarattini,_Remo2004" class="citation journal cs1">Garattini, Remo (2004). "How Spacetime Foam modifies the brick wall". <i><a href="/wiki/Modern_Physics_Letters_A" title="Modern Physics Letters A">Modern Physics Letters A</a></i>. <b>19</b> (36): <span class="nowrap">2673–</span>2682. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/0409015">gr-qc/0409015</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2004MPLA...19.2673G">2004MPLA...19.2673G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1142%2FS0217732304015658">10.1142/S0217732304015658</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:119094239">119094239</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Modern+Physics+Letters+A&rft.atitle=How+Spacetime+Foam+modifies+the+brick+wall&rft.volume=19&rft.issue=36&rft.pages=%3Cspan+class%3D%22nowrap%22%3E2673-%3C%2Fspan%3E2682&rft.date=2004&rft_id=info%3Aarxiv%2Fgr-qc%2F0409015&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119094239%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1142%2FS0217732304015658&rft_id=info%3Abibcode%2F2004MPLA...19.2673G&rft.au=Garattini%2C+Remo&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGonzález-Díaz,_Pedro_F.1998" class="citation journal cs1">González-Díaz, Pedro F. (1998). "Quantum time machine". <i><a href="/wiki/Physical_Review_D" class="mw-redirect" title="Physical Review D">Physical Review D</a></i>. <b>58</b> (12): 124011. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/9712033">gr-qc/9712033</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1998PhRvD..58l4011G">1998PhRvD..58l4011G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.58.124011">10.1103/PhysRevD.58.124011</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/10261%2F100644">10261/100644</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:28411713">28411713</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=Quantum+time+machine&rft.volume=58&rft.issue=12&rft.pages=124011&rft.date=1998&rft_id=info%3Ahdl%2F10261%2F100644&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A28411713%23id-name%3DS2CID&rft_id=info%3Abibcode%2F1998PhRvD..58l4011G&rft_id=info%3Aarxiv%2Fgr-qc%2F9712033&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.58.124011&rft.au=Gonz%C3%A1lez-D%C3%ADaz%2C+Pedro+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGonzález-Díaz,_Pedro_F.1996" class="citation journal cs1">González-Díaz, Pedro F. (1996). "Ringholes and closed timelike curves". <i><a href="/wiki/Physical_Review_D" class="mw-redirect" title="Physical Review D">Physical Review D</a></i>. <b>54</b> (10): <span class="nowrap">6122–</span>6131. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/9608059">gr-qc/9608059</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1996PhRvD..54.6122G">1996PhRvD..54.6122G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.54.6122">10.1103/PhysRevD.54.6122</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/10020617">10020617</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:7183386">7183386</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=Ringholes+and+closed+timelike+curves&rft.volume=54&rft.issue=10&rft.pages=%3Cspan+class%3D%22nowrap%22%3E6122-%3C%2Fspan%3E6131&rft.date=1996&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A7183386%23id-name%3DS2CID&rft_id=info%3Abibcode%2F1996PhRvD..54.6122G&rft_id=info%3Aarxiv%2Fgr-qc%2F9608059&rft_id=info%3Apmid%2F10020617&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.54.6122&rft.au=Gonz%C3%A1lez-D%C3%ADaz%2C+Pedro+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKhatsymosky,_Vladimir_M.1997" class="citation journal cs1">Khatsymosky, Vladimir M. (1997). "Towards possibility of self-maintained vacuum traversable wormhole". <i><a href="/wiki/Physics_Letters_B" class="mw-redirect" title="Physics Letters B">Physics Letters B</a></i>. <b>399</b> (<span class="nowrap">3–</span>4): <span class="nowrap">215–</span>222. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/9612013">gr-qc/9612013</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1997PhLB..399..215K">1997PhLB..399..215K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0370-2693%2897%2900290-6">10.1016/S0370-2693(97)00290-6</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:13917471">13917471</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Letters+B&rft.atitle=Towards+possibility+of+self-maintained+vacuum+traversable+wormhole&rft.volume=399&rft.issue=%3Cspan+class%3D%22nowrap%22%3E3%E2%80%93%3C%2Fspan%3E4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E215-%3C%2Fspan%3E222&rft.date=1997&rft_id=info%3Aarxiv%2Fgr-qc%2F9612013&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A13917471%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2FS0370-2693%2897%2900290-6&rft_id=info%3Abibcode%2F1997PhLB..399..215K&rft.au=Khatsymosky%2C+Vladimir+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKrasnikov,_Serguei2006" class="citation journal cs1">Krasnikov, Serguei (2006). "Counter example to a quantum inequality". <i><a href="/w/index.php?title=Gravity_and_Cosmology&action=edit&redlink=1" class="new" title="Gravity and Cosmology (page does not exist)">Gravity and Cosmology</a></i>. <b>46</b> (2006): 195. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/0409007">gr-qc/0409007</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2006GrCo...12..195K">2006GrCo...12..195K</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Gravity+and+Cosmology&rft.atitle=Counter+example+to+a+quantum+inequality&rft.volume=46&rft.issue=2006&rft.pages=195&rft.date=2006&rft_id=info%3Aarxiv%2Fgr-qc%2F0409007&rft_id=info%3Abibcode%2F2006GrCo...12..195K&rft.au=Krasnikov%2C+Serguei&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKrasnikov,_Serguei2003" class="citation journal cs1">Krasnikov, Serguei (2003). "The quantum inequalities do not forbid spacetime shortcuts". <i><a href="/wiki/Physical_Review_D" class="mw-redirect" title="Physical Review D">Physical Review D</a></i>. <b>67</b> (10): 104013. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/0207057">gr-qc/0207057</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2003PhRvD..67j4013K">2003PhRvD..67j4013K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.67.104013">10.1103/PhysRevD.67.104013</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:17498199">17498199</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=The+quantum+inequalities+do+not+forbid+spacetime+shortcuts&rft.volume=67&rft.issue=10&rft.pages=104013&rft.date=2003&rft_id=info%3Aarxiv%2Fgr-qc%2F0207057&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A17498199%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.67.104013&rft_id=info%3Abibcode%2F2003PhRvD..67j4013K&rft.au=Krasnikov%2C+Serguei&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLi,_Li-Xin2001" class="citation journal cs1">Li, Li-Xin (2001). "Two Open Universes Connected by a Wormhole: Exact Solutions". <i><a href="/wiki/Journal_of_Geometry_and_Physics" title="Journal of Geometry and Physics">Journal of Geometry and Physics</a></i>. <b>40</b> (2): <span class="nowrap">154–</span>160. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/hep-th/0102143">hep-th/0102143</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2001JGP....40..154L">2001JGP....40..154L</a>. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.267.8664">10.1.1.267.8664</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0393-0440%2801%2900028-6">10.1016/S0393-0440(01)00028-6</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:44433480">44433480</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Geometry+and+Physics&rft.atitle=Two+Open+Universes+Connected+by+a+Wormhole%3A+Exact+Solutions&rft.volume=40&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E154-%3C%2Fspan%3E160&rft.date=2001&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A44433480%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2001JGP....40..154L&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.267.8664%23id-name%3DCiteSeerX&rft_id=info%3Adoi%2F10.1016%2FS0393-0440%2801%2900028-6&rft_id=info%3Aarxiv%2Fhep-th%2F0102143&rft.au=Li%2C+Li-Xin&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMorris,_Michael_S.Thorne,_Kip_S.Yurtsever,_Ulvi1988" class="citation journal cs1">Morris, Michael S.; Thorne, Kip S. & Yurtsever, Ulvi (1988). <a rel="nofollow" class="external text" href="https://authors.library.caltech.edu/9262/1/MORprl88.pdf">"Wormholes, Time Machines, and the Weak Energy Condition"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/Physical_Review_Letters" title="Physical Review Letters">Physical Review Letters</a></i>. <b>61</b> (13): <span class="nowrap">1446–</span>1449. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1988PhRvL..61.1446M">1988PhRvL..61.1446M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.61.1446">10.1103/PhysRevLett.61.1446</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/10038800">10038800</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Wormholes%2C+Time+Machines%2C+and+the+Weak+Energy+Condition&rft.volume=61&rft.issue=13&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1446-%3C%2Fspan%3E1449&rft.date=1988&rft_id=info%3Apmid%2F10038800&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.61.1446&rft_id=info%3Abibcode%2F1988PhRvL..61.1446M&rft.au=Morris%2C+Michael+S.&rft.au=Thorne%2C+Kip+S.&rft.au=Yurtsever%2C+Ulvi&rft_id=https%3A%2F%2Fauthors.library.caltech.edu%2F9262%2F1%2FMORprl88.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMorris,_Michael_S.Thorne,_Kip_S.1988" class="citation journal cs1">Morris, Michael S. & Thorne, Kip S. (1988). <a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.15620">"Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity"</a>. <i><a href="/wiki/American_Journal_of_Physics" title="American Journal of Physics">American Journal of Physics</a></i>. <b>56</b> (5): <span class="nowrap">395–</span>412. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1988AmJPh..56..395M">1988AmJPh..56..395M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.15620">10.1119/1.15620</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=Wormholes+in+spacetime+and+their+use+for+interstellar+travel%3A+A+tool+for+teaching+general+relativity&rft.volume=56&rft.issue=5&rft.pages=%3Cspan+class%3D%22nowrap%22%3E395-%3C%2Fspan%3E412&rft.date=1988&rft_id=info%3Adoi%2F10.1119%2F1.15620&rft_id=info%3Abibcode%2F1988AmJPh..56..395M&rft.au=Morris%2C+Michael+S.&rft.au=Thorne%2C+Kip+S.&rft_id=https%3A%2F%2Fdoi.org%2F10.1119%252F1.15620&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNandi,_Kamal_K.Zhang,_Yuan-Zhong2006" class="citation journal cs1">Nandi, Kamal K. & Zhang, Yuan-Zhong (2006). "A Quantum Constraint for the Physical Viability of Classical Traversable Lorentzian Wormholes". <i><a href="/w/index.php?title=Journal_of_Nonlinear_Phenomena_in_Complex_Systems&action=edit&redlink=1" class="new" title="Journal of Nonlinear Phenomena in Complex Systems (page does not exist)">Journal of Nonlinear Phenomena in Complex Systems</a></i>. <b>9</b> (2006): <span class="nowrap">61–</span>67. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/0409053">gr-qc/0409053</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2004gr.qc.....9053N">2004gr.qc.....9053N</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Nonlinear+Phenomena+in+Complex+Systems&rft.atitle=A+Quantum+Constraint+for+the+Physical+Viability+of+Classical+Traversable+Lorentzian+Wormholes&rft.volume=9&rft.issue=2006&rft.pages=%3Cspan+class%3D%22nowrap%22%3E61-%3C%2Fspan%3E67&rft.date=2006&rft_id=info%3Aarxiv%2Fgr-qc%2F0409053&rft_id=info%3Abibcode%2F2004gr.qc.....9053N&rft.au=Nandi%2C+Kamal+K.&rft.au=Zhang%2C+Yuan-Zhong&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOri,_Amos2005" class="citation journal cs1">Ori, Amos (2005). "A new time-machine model with compact vacuum core". <i><a href="/wiki/Physical_Review_Letters" title="Physical Review Letters">Physical Review Letters</a></i>. <b>95</b> (2): 021101. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/0503077">gr-qc/0503077</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2005PhRvL..95b1101O">2005PhRvL..95b1101O</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.95.021101">10.1103/PhysRevLett.95.021101</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/16090670">16090670</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=A+new+time-machine+model+with+compact+vacuum+core&rft.volume=95&rft.issue=2&rft.pages=021101&rft.date=2005&rft_id=info%3Aarxiv%2Fgr-qc%2F0503077&rft_id=info%3Apmid%2F16090670&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.95.021101&rft_id=info%3Abibcode%2F2005PhRvL..95b1101O&rft.au=Ori%2C+Amos&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRoman,_Thomas_A.2004" class="citation journal cs1">Roman, Thomas A. (2004). "Some Thoughts on Energy Conditions and Wormholes". <i>The Tenth Marcel Grossmann Meeting</i>: <span class="nowrap">1909–</span>1924. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/0409090">gr-qc/0409090</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1142%2F9789812704030_0236">10.1142/9789812704030_0236</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-981-256-667-6" title="Special:BookSources/978-981-256-667-6"><bdi>978-981-256-667-6</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:18867900">18867900</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Tenth+Marcel+Grossmann+Meeting&rft.atitle=Some+Thoughts+on+Energy+Conditions+and+Wormholes&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1909-%3C%2Fspan%3E1924&rft.date=2004&rft_id=info%3Aarxiv%2Fgr-qc%2F0409090&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A18867900%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1142%2F9789812704030_0236&rft.isbn=978-981-256-667-6&rft.au=Roman%2C+Thomas+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTeo,_Edward1998" class="citation journal cs1">Teo, Edward (1998). "Rotating traversable wormholes". <i><a href="/wiki/Physical_Review_D" class="mw-redirect" title="Physical Review D">Physical Review D</a></i>. <b>58</b> (2): 024014. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/9803098">gr-qc/9803098</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1998PhRvD..58b4014T">1998PhRvD..58b4014T</a>. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.339.966">10.1.1.339.966</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.58.024014">10.1103/PhysRevD.58.024014</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:15316540">15316540</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=Rotating+traversable+wormholes&rft.volume=58&rft.issue=2&rft.pages=024014&rft.date=1998&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A15316540%23id-name%3DS2CID&rft_id=info%3Abibcode%2F1998PhRvD..58b4014T&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.339.966%23id-name%3DCiteSeerX&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.58.024014&rft_id=info%3Aarxiv%2Fgr-qc%2F9803098&rft.au=Teo%2C+Edward&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVisser,_Matt2002" class="citation arxiv cs1">Visser, Matt (2002). "The quantum physics of chronology protection by Matt Visser". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/0204022">gr-qc/0204022</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=The+quantum+physics+of+chronology+protection+by+Matt+Visser&rft.date=2002&rft_id=info%3Aarxiv%2Fgr-qc%2F0204022&rft.au=Visser%2C+Matt&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span> An excellent and more concise review.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVisser,_Matt1989" class="citation journal cs1">Visser, Matt (1989). "Traversable wormholes: Some simple examples". <i><a href="/wiki/Physical_Review_D" class="mw-redirect" title="Physical Review D">Physical Review D</a></i>. <b>39</b> (10): <span class="nowrap">3182–</span>3184. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/0809.0907">0809.0907</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1989PhRvD..39.3182V">1989PhRvD..39.3182V</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.39.3182">10.1103/PhysRevD.39.3182</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/9959561">9959561</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:17949528">17949528</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=Traversable+wormholes%3A+Some+simple+examples&rft.volume=39&rft.issue=10&rft.pages=%3Cspan+class%3D%22nowrap%22%3E3182-%3C%2Fspan%3E3184&rft.date=1989&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A17949528%23id-name%3DS2CID&rft_id=info%3Abibcode%2F1989PhRvD..39.3182V&rft_id=info%3Aarxiv%2F0809.0907&rft_id=info%3Apmid%2F9959561&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.39.3182&rft.au=Visser%2C+Matt&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWormhole" class="Z3988"></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wormhole&action=edit&section=20" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Wormholes" class="extiw" title="commons:Category:Wormholes">Wormholes</a></span>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://www.scientificamerican.com/article/follow-up-what-exactly-is/">"What exactly is a 'wormhole'? Have wormholes been proven to exist or are they still theoretical??"</a> answered by Richard F. Holman, William A. Hiscock and Matt Visser</li> <li><a rel="nofollow" class="external text" href="http://homepages.mcs.vuw.ac.nz/~visser/general.shtml#why-wormholes">"Why wormholes?"</a> by Matt Visser (October 1996)</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20120222034225/http://www.bun.kyoto-u.ac.jp/~suchii/wormholes.html">Wormholes in General Relativity by Soshichi Uchii</a> at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> (archived February 22, 2012)</li> <li><a rel="nofollow" class="external text" href="http://www.webfilesuci.org/WormholeFAQ.html">Questions and Answers about Wormholes</a> – A comprehensive wormhole FAQ by Enrico Rodrigo</li> <li><a rel="nofollow" class="external text" href="http://www.spacetimetravel.org/wurmlochflug/wurmlochflug.html">animation that simulates traversing a wormhole</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20151228145356/https://www.vis.uni-stuttgart.de/~muelleta/MTvis/">Renderings and animations of a Morris-Thorne wormhole</a></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Black_holes386" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3" style="text-align:center;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Black_holes" title="Template:Black holes"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Black_holes" title="Template talk:Black holes"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Black_holes" title="Special:EditPage/Template:Black holes"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Black_holes386" style="font-size:114%;margin:0 4em"><a href="/wiki/Black_hole" title="Black hole">Black holes</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="3" style="text-align:center;"><div> <ul><li><a href="/wiki/Outline_of_black_holes" title="Outline of black holes">Outline</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Types</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/BTZ_black_hole" title="BTZ black hole">BTZ black hole</a></li> <li><a href="/wiki/Schwarzschild_metric" title="Schwarzschild metric">Schwarzschild</a></li> <li><a href="/wiki/Rotating_black_hole" title="Rotating black hole">Rotating</a></li> <li><a href="/wiki/Charged_black_hole" title="Charged black hole">Charged</a></li> <li><a href="/wiki/Virtual_black_hole" title="Virtual black hole">Virtual</a></li> <li><a href="/wiki/Kugelblitz_(astrophysics)" title="Kugelblitz (astrophysics)">Kugelblitz</a></li> <li><a href="/wiki/Supermassive_black_hole" title="Supermassive black hole">Supermassive</a></li> <li><a href="/wiki/Primordial_black_hole" title="Primordial black hole">Primordial</a></li> <li><a href="/wiki/Direct_collapse_black_hole" title="Direct collapse black hole">Direct collapse</a></li> <li><a href="/wiki/Rogue_black_hole" title="Rogue black hole">Rogue</a></li> <li><a href="/wiki/Malament%E2%80%93Hogarth_spacetime" title="Malament–Hogarth spacetime">Malament–Hogarth spacetime</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="11" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Black_hole_-_Messier_87_crop_max_res.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Black_hole_-_Messier_87_crop_max_res.jpg/80px-Black_hole_-_Messier_87_crop_max_res.jpg" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Black_hole_-_Messier_87_crop_max_res.jpg/120px-Black_hole_-_Messier_87_crop_max_res.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Black_hole_-_Messier_87_crop_max_res.jpg/160px-Black_hole_-_Messier_87_crop_max_res.jpg 2x" data-file-width="4320" data-file-height="4320" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Size</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Micro_black_hole" title="Micro black hole">Micro</a> <ul><li><a href="/wiki/Extremal_black_hole" title="Extremal black hole">Extremal</a></li> <li><a href="/wiki/Black_hole_electron" title="Black hole electron">Electron</a></li></ul></li> <li><a href="/wiki/Stellar_black_hole" title="Stellar black hole">Stellar</a> <ul><li><a href="/wiki/Microquasar" title="Microquasar">Microquasar</a></li></ul></li> <li><a href="/wiki/Intermediate-mass_black_hole" title="Intermediate-mass black hole">Intermediate-mass</a></li> <li><a href="/wiki/Supermassive_black_hole" title="Supermassive black hole">Supermassive</a> <ul><li><a href="/wiki/Active_galactic_nucleus" title="Active galactic nucleus">Active galactic nucleus</a></li> <li><a href="/wiki/Quasar" title="Quasar">Quasar</a></li> <li><a href="/wiki/Large_quasar_group" title="Large quasar group">LQG</a></li> <li><a href="/wiki/Blazar" title="Blazar">Blazar</a></li> <li><a href="/wiki/OVV_quasar" title="OVV quasar">OVV</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Formation</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Stellar_evolution" title="Stellar evolution">Stellar evolution</a></li> <li><a href="/wiki/Gravitational_collapse" title="Gravitational collapse">Gravitational collapse</a></li> <li><a href="/wiki/Neutron_star" title="Neutron star">Neutron star</a> <ul><li><a href="/wiki/Template:Neutron_star" title="Template:Neutron star">Related links</a></li></ul></li> <li><a href="/wiki/Tolman%E2%80%93Oppenheimer%E2%80%93Volkoff_limit" title="Tolman–Oppenheimer–Volkoff limit">Tolman–Oppenheimer–Volkoff limit</a></li> <li><a href="/wiki/White_dwarf" title="White dwarf">White dwarf</a> <ul><li><a href="/wiki/Template:White_dwarf" title="Template:White dwarf">Related links</a></li></ul></li> <li><a href="/wiki/Supernova" title="Supernova">Supernova</a> <ul><li><a href="/wiki/Micronova" title="Micronova">Micronova</a></li> <li><a href="/wiki/Superluminous_supernova" title="Superluminous supernova">Hypernova</a></li> <li><a href="/wiki/Template:Supernovae" title="Template:Supernovae">Related links</a></li></ul></li> <li><a href="/wiki/Gamma-ray_burst" title="Gamma-ray burst">Gamma-ray burst</a></li> <li><a href="/wiki/Binary_black_hole" title="Binary black hole">Binary black hole</a></li> <li><a href="/wiki/Quark_star" title="Quark star">Quark star</a></li> <li><a href="/wiki/Supermassive_star" class="mw-redirect" title="Supermassive star">Supermassive star</a></li> <li><a href="/wiki/Quasi-star" title="Quasi-star">Quasi-star</a></li> <li><a href="/wiki/Dark_star_(dark_matter)" title="Dark star (dark matter)">Supermassive dark star</a></li> <li><a href="/wiki/X-ray_binary" title="X-ray binary">X-ray binary</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Properties</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Astrophysical_jet" title="Astrophysical jet">Astrophysical jet</a></li> <li><a href="/wiki/Gravitational_singularity" title="Gravitational singularity">Gravitational singularity</a> <ul><li><a href="/wiki/Ring_singularity" title="Ring singularity">Ring singularity</a></li> <li><a href="/wiki/Penrose%E2%80%93Hawking_singularity_theorems" title="Penrose–Hawking singularity theorems">Theorems</a></li></ul></li> <li><a href="/wiki/Event_horizon" title="Event horizon">Event horizon</a></li> <li><a href="/wiki/Photon_sphere" title="Photon sphere">Photon sphere</a></li> <li><a href="/wiki/Innermost_stable_circular_orbit" title="Innermost stable circular orbit">Innermost stable circular orbit</a></li> <li><a href="/wiki/Ergosphere" title="Ergosphere">Ergosphere</a> <ul><li><a href="/wiki/Penrose_process" title="Penrose process">Penrose process</a></li> <li><a href="/wiki/Blandford%E2%80%93Znajek_process" title="Blandford–Znajek process">Blandford–Znajek process</a></li></ul></li> <li><a href="/wiki/Accretion_disk" title="Accretion disk">Accretion disk</a></li> <li><a href="/wiki/Hawking_radiation" title="Hawking radiation">Hawking radiation</a></li> <li><a href="/wiki/Gravitational_lens" title="Gravitational lens">Gravitational lens</a> <ul><li><a href="/wiki/Gravitational_microlensing" title="Gravitational microlensing">Microlens</a></li></ul></li> <li><a href="/wiki/Bondi_accretion" title="Bondi accretion">Bondi accretion</a></li> <li><a href="/wiki/M%E2%80%93sigma_relation" title="M–sigma relation">M–sigma relation</a></li> <li><a href="/wiki/Quasi-periodic_oscillation" class="mw-redirect" title="Quasi-periodic oscillation">Quasi-periodic oscillation</a></li> <li><a href="/wiki/Black_hole_thermodynamics" title="Black hole thermodynamics">Thermodynamics</a></li> <li><a href="/wiki/Bekenstein_bound" title="Bekenstein bound">Bekenstein bound</a></li> <li><a href="/wiki/Bousso%27s_holographic_bound" title="Bousso's holographic bound">Bousso's holographic bound</a> <ul><li><a href="/wiki/Immirzi_parameter" title="Immirzi parameter">Immirzi parameter</a></li></ul></li> <li><a href="/wiki/Schwarzschild_radius" title="Schwarzschild radius">Schwarzschild radius</a></li> <li><a href="/wiki/Spaghettification" title="Spaghettification">Spaghettification</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Issues</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Black_hole_complementarity" title="Black hole complementarity">Black hole complementarity</a></li> <li><a href="/wiki/Black_hole_information_paradox" title="Black hole information paradox">Information paradox</a></li> <li><a href="/wiki/Cosmic_censorship_hypothesis" title="Cosmic censorship hypothesis">Cosmic censorship</a></li> <li><a href="/wiki/ER_%3D_EPR" title="ER = EPR">ER = EPR</a></li> <li><a href="/wiki/Binary_black_hole#Final_parsec_problem" title="Binary black hole">Final parsec problem</a></li> <li><a href="/wiki/Firewall_(physics)" title="Firewall (physics)">Firewall (physics)</a></li> <li><a href="/wiki/Holographic_principle" title="Holographic principle">Holographic principle</a></li> <li><a href="/wiki/No-hair_theorem" title="No-hair theorem">No-hair theorem</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Metrics</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Schwarzschild_metric" title="Schwarzschild metric">Schwarzschild</a> (<a href="/wiki/Derivation_of_the_Schwarzschild_solution" title="Derivation of the Schwarzschild solution">Derivation</a>)</li> <li><a href="/wiki/Kerr_metric" title="Kerr metric">Kerr</a></li> <li><a href="/wiki/Reissner%E2%80%93Nordstr%C3%B6m_metric" title="Reissner–Nordström metric">Reissner–Nordström</a></li> <li><a href="/wiki/Kerr%E2%80%93Newman_metric" title="Kerr–Newman metric">Kerr–Newman</a></li> <li><a href="/wiki/Hayward_metric" title="Hayward metric">Hayward</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Alternatives</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Nonsingular_black_hole_models" title="Nonsingular black hole models">Nonsingular black hole models</a></li> <li><a href="/wiki/Black_star_(semiclassical_gravity)" title="Black star (semiclassical gravity)">Black star</a></li> <li><a href="/wiki/Dark_star_(Newtonian_mechanics)" title="Dark star (Newtonian mechanics)">Dark star</a></li> <li><a href="/wiki/Dark-energy_star" title="Dark-energy star">Dark-energy star</a></li> <li><a href="/wiki/Gravastar" title="Gravastar">Gravastar</a></li> <li><a href="/wiki/Magnetospheric_eternally_collapsing_object" title="Magnetospheric eternally collapsing object">Magnetospheric eternally collapsing object</a></li> <li><a href="/wiki/Planck_star" title="Planck star">Planck star</a></li> <li><a href="/wiki/Q_star" title="Q star">Q star</a></li> <li><a href="/wiki/Fuzzball_(string_theory)" title="Fuzzball (string theory)">Fuzzball</a></li> <li><a href="/wiki/Geon_(physics)" title="Geon (physics)">Geon</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Analogs</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Optical_black_hole" title="Optical black hole">Optical black hole</a></li> <li><a href="/wiki/Sonic_black_hole" title="Sonic black hole">Sonic black hole</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Lists_of_black_holes" title="Lists of black holes">Lists</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_black_holes" title="List of black holes">Black holes</a></li> <li><a href="/wiki/List_of_most_massive_black_holes" title="List of most massive black holes">Most massive</a></li> <li><a href="/wiki/List_of_nearest_known_black_holes" title="List of nearest known black holes">Nearest</a></li> <li><a href="/wiki/List_of_quasars" title="List of quasars">Quasars</a></li> <li><a href="/wiki/List_of_microquasars" title="List of microquasars">Microquasars</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Outline_of_black_holes" title="Outline of black holes">Outline of black holes</a></li> <li><a href="/wiki/Black_Hole_Initiative" title="Black Hole Initiative">Black Hole Initiative</a></li> <li><a href="/wiki/Black_hole_starship" title="Black hole starship">Black hole starship</a></li> <li><a href="/wiki/Black_holes_in_fiction" title="Black holes in fiction">Black holes in fiction</a></li> <li><a href="/wiki/Big_Bang" title="Big Bang">Big Bang</a></li> <li><a href="/wiki/Big_Bounce" title="Big Bounce">Big Bounce</a></li> <li><a href="/wiki/Compact_star" class="mw-redirect" title="Compact star">Compact star</a></li> <li><a href="/wiki/Exotic_star" title="Exotic star">Exotic star</a> <ul><li><a href="/wiki/Quark_star" title="Quark star">Quark star</a></li> <li><a href="/wiki/Preon_star" class="mw-redirect" title="Preon star">Preon star</a></li></ul></li> <li><a href="/wiki/Gravitational_waves" class="mw-redirect" title="Gravitational waves">Gravitational waves</a></li> <li><a href="/wiki/Gamma-ray_burst_progenitors" title="Gamma-ray burst progenitors">Gamma-ray burst progenitors</a></li> <li><a href="/wiki/Gravity_well" class="mw-redirect" title="Gravity well">Gravity well</a></li> <li><a href="/wiki/Hypercompact_stellar_system" title="Hypercompact stellar system">Hypercompact stellar system</a></li> <li><a href="/wiki/Membrane_paradigm" title="Membrane paradigm">Membrane paradigm</a></li> <li><a href="/wiki/Naked_singularity" title="Naked singularity">Naked singularity</a></li> <li><a href="/wiki/Population_III_star" class="mw-redirect" title="Population III star">Population III star</a></li> <li><a href="/wiki/Supermassive_star" class="mw-redirect" title="Supermassive star">Supermassive star</a></li> <li><a href="/wiki/Quasi-star" title="Quasi-star">Quasi-star</a></li> <li><a href="/wiki/Dark_star_(dark_matter)" title="Dark star (dark matter)">Supermassive dark star</a></li> <li><a href="/wiki/Rossi_X-ray_Timing_Explorer" title="Rossi X-ray Timing Explorer">Rossi X-ray Timing Explorer</a></li> <li><a href="/wiki/Superluminal_motion" title="Superluminal motion">Superluminal motion</a></li> <li><a href="/wiki/Timeline_of_black_hole_physics" title="Timeline of black hole physics">Timeline of black hole physics</a></li> <li><a href="/wiki/White_hole" title="White hole">White hole</a></li> <li><a class="mw-selflink selflink">Wormhole</a></li> <li><a href="/wiki/Tidal_disruption_event" title="Tidal disruption event">Tidal disruption event</a></li> <li><a href="/wiki/Planet_Nine" title="Planet Nine">Planet Nine</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Notable</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cygnus_X-1" title="Cygnus X-1">Cygnus X-1</a></li> <li><a href="/wiki/XTE_J1650-500" class="mw-redirect" title="XTE J1650-500">XTE J1650-500</a></li> <li><a href="/wiki/XTE_J1118%2B480" title="XTE J1118+480">XTE J1118+480</a></li> <li><a href="/wiki/A0620-00" title="A0620-00">A0620-00</a></li> <li><a href="/wiki/Sagittarius_A*" title="Sagittarius A*">Sagittarius A*</a></li> <li><a href="/wiki/Centaurus_A" title="Centaurus A">Centaurus A</a></li> <li><a href="/wiki/Phoenix_Cluster" title="Phoenix Cluster">Phoenix Cluster</a></li> <li><a href="/wiki/PKS_1302-102" class="mw-redirect" title="PKS 1302-102">PKS 1302-102</a></li> <li><a href="/wiki/OJ_287" title="OJ 287">OJ 287</a></li> <li><a href="/wiki/SDSS_J0849%2B1114" title="SDSS J0849+1114">SDSS J0849+1114</a></li> <li><a href="/wiki/TON_618" title="TON 618">TON 618</a></li> <li><a href="/wiki/MS_0735.6%2B7421" title="MS 0735.6+7421">MS 0735.6+7421</a></li> <li><a href="/wiki/NeVe_1" title="NeVe 1">NeVe 1</a></li> <li><a href="/wiki/Hercules_A" title="Hercules A">Hercules A</a></li> <li><a href="/wiki/3C_273" title="3C 273">3C 273</a></li> <li><a href="/wiki/Q0906%2B6930" title="Q0906+6930">Q0906+6930</a></li> <li><a href="/wiki/Markarian_501" title="Markarian 501">Markarian 501</a></li> <li><a href="/wiki/ULAS_J1342%2B0928" title="ULAS J1342+0928">ULAS J1342+0928</a></li> <li><a href="/wiki/PSO_J030947.49%2B271757.31" title="PSO J030947.49+271757.31">PSO J030947.49+271757.31</a></li> <li><a href="/wiki/AT2018hyz" title="AT2018hyz">AT2018hyz</a></li> <li><a href="/wiki/Swift_J1644%2B57" title="Swift J1644+57">Swift J1644+57</a></li> <li><a href="/wiki/1ES_1927%2B654" title="1ES 1927+654">1ES 1927+654</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="3" style="text-align:center;"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Black_holes" title="Category:Black holes">Category</a></li> <li><span class="noviewer" typeof="mw:File"><span title="Commons page"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> <a href="https://commons.wikimedia.org/wiki/Category:Black_holes" class="extiw" title="commons:Category:Black holes">Commons</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Time_travel73" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Time_travel" title="Template:Time travel"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Time_travel" title="Template talk:Time travel"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Time_travel" title="Special:EditPage/Template:Time travel"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Time_travel73" style="font-size:114%;margin:0 4em"><a href="/wiki/Time_travel" title="Time travel">Time travel</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">General terms and concepts</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chronology_protection_conjecture" title="Chronology protection conjecture">Chronology protection conjecture</a></li> <li><a href="/wiki/Closed_timelike_curve" title="Closed timelike curve">Closed timelike curve</a></li> <li><a href="/wiki/Novikov_self-consistency_principle" title="Novikov self-consistency principle">Novikov self-consistency principle</a></li> <li><a href="/wiki/Self-fulfilling_prophecy#Causal_loop" title="Self-fulfilling prophecy">Self-fulfilling prophecy</a></li> <li><a href="/wiki/Quantum_mechanics_of_time_travel" title="Quantum mechanics of time travel">Quantum mechanics of time travel</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Philosophy_of_space_and_time" title="Philosophy of space and time">Philosophy of space and time</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Butterfly_effect" title="Butterfly effect">Butterfly effect</a></li> <li><a href="/wiki/Determinism" title="Determinism">Determinism</a></li> <li><a href="/wiki/Eternalism_(philosophy_of_time)" title="Eternalism (philosophy of time)">Eternalism</a></li> <li><a href="/wiki/Fatalism" title="Fatalism">Fatalism</a></li> <li><a href="/wiki/Free_will" title="Free will">Free will</a></li> <li><a href="/wiki/Predestination" title="Predestination">Predestination</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Causality</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Causal_loop" class="mw-redirect" title="Causal loop">Causal loop</a></li> <li><a href="/wiki/Causality_(physics)" title="Causality (physics)">Causality (physics)</a></li> <li><a href="/wiki/Chronology_protection_conjecture" title="Chronology protection conjecture">Chronology protection conjecture</a></li> <li><a href="/wiki/Cosmic_censorship_hypothesis" title="Cosmic censorship hypothesis">Cosmic censorship hypothesis</a></li> <li><a href="/wiki/The_chicken_or_the_egg" class="mw-redirect" title="The chicken or the egg">The chicken or the egg</a></li> <li><a href="/wiki/Many-worlds_interpretation" title="Many-worlds interpretation">Many-worlds interpretation</a></li> <li><a href="/wiki/Grandfather_paradox" class="mw-redirect" title="Grandfather paradox">Grandfather paradox</a></li> <li><a href="/wiki/Quantum_mechanics_of_time_travel" title="Quantum mechanics of time travel">Quantum mechanics of time travel</a></li> <li><a href="/wiki/Time_viewer" title="Time viewer">Time viewer</a></li> <li><a href="/wiki/Temporal_paradox" title="Temporal paradox">Temporal paradox</a></li> <li><a href="/wiki/Temporal_paradox#Grandfather_paradox" title="Temporal paradox">Grandfather paradox</a></li> <li><a href="/wiki/Time_loop" title="Time loop">Time loop</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Time_travel_in_fiction" title="Time travel in fiction">Time travel in fiction</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_timelines#Fictional" title="List of timelines">Timelines in fiction</a></li> <li><a href="/wiki/List_of_time_travel_works_of_fiction" title="List of time travel works of fiction">Time travel in fiction</a></li> <li><a href="/wiki/List_of_films_featuring_time_loops" title="List of films featuring time loops">Time loops in film</a></li> <li><i>Major works:</i></li> <li><a href="/wiki/The_Time_Machine" title="The Time Machine">The Time Machine</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Parallel timelines</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Time_travel_in_fiction#Alternative_future,_history,_timelines,_and_dimensions" title="Time travel in fiction">Alternative future</a></li> <li><a href="/wiki/Alternate_history" title="Alternate history">Alternate history</a></li> <li><a href="/wiki/Many-worlds_interpretation" title="Many-worlds interpretation">Many-worlds interpretation</a></li> <li><a href="/wiki/Multiverse" title="Multiverse">Multiverse</a></li> <li><a href="/wiki/Parallel_universes_in_fiction" title="Parallel universes in fiction">Parallel universes in fiction</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Spacetime" title="Spacetime">Spacetimes</a> in <a href="/wiki/General_relativity" title="General relativity">general relativity</a> that<br /> can contain <a href="/wiki/Closed_timelike_curve" title="Closed timelike curve">closed timelike curves</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alcubierre_drive" title="Alcubierre drive">Alcubierre metric</a></li> <li><a href="/wiki/BTZ_black_hole" title="BTZ black hole">BTZ black hole</a></li> <li><a href="/wiki/G%C3%B6del_metric" title="Gödel metric">Gödel metric</a></li> <li><a href="/wiki/Kerr_metric" title="Kerr metric">Kerr metric</a></li> <li><a href="/wiki/Krasnikov_tube" title="Krasnikov tube">Krasnikov tube</a></li> <li><a href="/wiki/Misner_space" title="Misner space">Misner space</a></li> <li><a href="/wiki/Tipler_cylinder" title="Tipler cylinder">Tipler cylinder</a></li> <li><a href="/wiki/Van_Stockum_dust" title="Van Stockum dust">van Stockum dust</a></li> <li><a class="mw-selflink-fragment" href="#Traversable_wormholes">Traversable wormholes</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Science_fiction" title="Science fiction">Science fiction</a></li> <li><a href="/wiki/Time_machine" class="mw-redirect" title="Time machine">Time machine</a></li> <li><a class="mw-selflink selflink">Wormhole</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q7544#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata1126" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q7544#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata1126" style="font-size:114%;margin:0 4em"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q7544#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/1141807319">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh2004010731">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb159222287">France</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb159222287">BnF data</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="červí díry"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph220674&CON_LNG=ENG">Czech Republic</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.nli.org.il/en/authorities/987007532742605171">Israel</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.idref.fr/131066986">IdRef</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Wormhole&oldid=1276143628">https://en.wikipedia.org/w/index.php?title=Wormhole&oldid=1276143628</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Wormhole_theory" title="Category:Wormhole theory">Wormhole theory</a></li><li><a href="/wiki/Category:Albert_Einstein" title="Category:Albert Einstein">Albert Einstein</a></li><li><a href="/wiki/Category:Astronomical_hypotheses" title="Category:Astronomical hypotheses">Astronomical hypotheses</a></li><li><a href="/wiki/Category:Black_holes" title="Category:Black holes">Black holes</a></li><li><a href="/wiki/Category:Conjectures" title="Category:Conjectures">Conjectures</a></li><li><a href="/wiki/Category:Exotic_matter" title="Category:Exotic matter">Exotic matter</a></li><li><a href="/wiki/Category:Faster-than-light_travel" title="Category:Faster-than-light travel">Faster-than-light travel</a></li><li><a href="/wiki/Category:General_relativity" title="Category:General relativity">General relativity</a></li><li><a href="/wiki/Category:Gravity" title="Category:Gravity">Gravity</a></li><li><a href="/wiki/Category:Hypothetical_astronomical_objects" title="Category:Hypothetical astronomical objects">Hypothetical astronomical objects</a></li><li><a href="/wiki/Category:Lorentzian_manifolds" title="Category:Lorentzian manifolds">Lorentzian manifolds</a></li><li><a href="/wiki/Category:Space" title="Category:Space">Space</a></li><li><a href="/wiki/Category:Theory_of_relativity" title="Category:Theory of relativity">Theory of relativity</a></li><li><a href="/wiki/Category:Time_travel" title="Category:Time travel">Time travel</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:CS1_maint:_location_missing_publisher" title="Category:CS1 maint: location missing publisher">CS1 maint: location missing publisher</a></li><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_matches_Wikidata" title="Category:Short description matches Wikidata">Short description matches Wikidata</a></li><li><a href="/wiki/Category:All_articles_with_unsourced_statements" title="Category:All articles with unsourced statements">All articles with unsourced statements</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_August_2023" title="Category:Articles with unsourced statements from August 2023">Articles with unsourced statements from August 2023</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_February_2025" title="Category:Articles with unsourced statements from February 2025">Articles with unsourced statements from February 2025</a></li><li><a href="/wiki/Category:Wikipedia_articles_needing_clarification_from_March_2017" title="Category:Wikipedia articles needing clarification from March 2017">Wikipedia articles needing clarification from March 2017</a></li><li><a href="/wiki/Category:Wikipedia_articles_needing_page_number_citations_from_January_2018" title="Category:Wikipedia articles needing page number citations from January 2018">Wikipedia articles needing page number citations from January 2018</a></li><li><a href="/wiki/Category:Commons_category_link_is_on_Wikidata" title="Category:Commons category link is on Wikidata">Commons category link is on Wikidata</a></li><li><a href="/wiki/Category:Webarchive_template_wayback_links" title="Category:Webarchive template wayback links">Webarchive template wayback links</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 17 February 2025, at 03:45<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. By using this site, you agree to the <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use" class="extiw" title="foundation:Special:MyLanguage/Policy:Terms of Use">Terms of Use</a> and <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy" class="extiw" title="foundation:Special:MyLanguage/Policy:Privacy policy">Privacy Policy</a>. Wikipedia® is a registered trademark of the <a rel="nofollow" class="external text" href="https://wikimediafoundation.org/">Wikimedia Foundation, Inc.</a>, a non-profit organization.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacy policy</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:About">About Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:General_disclaimer">Disclaimers</a></li> <li id="footer-places-contact"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us">Contact Wikipedia</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Developers</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/en.wikipedia.org">Statistics</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie statement</a></li> <li id="footer-places-mobileview"><a href="//en.m.wikipedia.org/w/index.php?title=Wormhole&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobile view</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" lang="en" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><picture><source media="(min-width: 500px)" srcset="/w/resources/assets/poweredby_mediawiki.svg" width="88" height="31"><img src="/w/resources/assets/mediawiki_compact.svg" alt="Powered by MediaWiki" width="25" height="25" loading="lazy"></picture></a></li> </ul> </footer> </div> </div> </div> <div class="vector-header-container vector-sticky-header-container"> <div id="vector-sticky-header" class="vector-sticky-header"> <div class="vector-sticky-header-start"> <div class="vector-sticky-header-icon-start vector-button-flush-left vector-button-flush-right" aria-hidden="true"> <button class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-sticky-header-search-toggle" tabindex="-1" data-event-name="ui.vector-sticky-search-form.icon"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </button> </div> <div role="search" class="vector-search-box-vue vector-search-box-show-thumbnail vector-search-box"> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail"> <form action="/w/index.php" id="vector-sticky-search-form" class="cdx-search-input cdx-search-input--has-end-button"> <div class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia"> <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <div class="vector-sticky-header-context-bar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-sticky-header-toc" class="vector-dropdown mw-portlet mw-portlet-sticky-header-toc vector-sticky-header-toc vector-button-flush-left" > <input type="checkbox" id="vector-sticky-header-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-sticky-header-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-sticky-header-toc-label" for="vector-sticky-header-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-sticky-header-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div class="vector-sticky-header-context-bar-primary" aria-hidden="true" ><span class="mw-page-title-main">Wormhole</span></div> </div> </div> <div class="vector-sticky-header-end" aria-hidden="true"> <div class="vector-sticky-header-icons"> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-talk-sticky-header" tabindex="-1" data-event-name="talk-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbles mw-ui-icon-wikimedia-speechBubbles"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-subject-sticky-header" tabindex="-1" data-event-name="subject-sticky-header"><span class="vector-icon mw-ui-icon-article mw-ui-icon-wikimedia-article"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-history-sticky-header" tabindex="-1" data-event-name="history-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-history mw-ui-icon-wikimedia-wikimedia-history"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only mw-watchlink" id="ca-watchstar-sticky-header" tabindex="-1" data-event-name="watch-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-star mw-ui-icon-wikimedia-wikimedia-star"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-edit-sticky-header" tabindex="-1" data-event-name="wikitext-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-wikiText mw-ui-icon-wikimedia-wikimedia-wikiText"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-ve-edit-sticky-header" tabindex="-1" data-event-name="ve-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-edit mw-ui-icon-wikimedia-wikimedia-edit"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-viewsource-sticky-header" tabindex="-1" data-event-name="ve-edit-protected-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-editLock mw-ui-icon-wikimedia-wikimedia-editLock"></span> <span></span> </a> </div> <div class="vector-sticky-header-buttons"> <button class="cdx-button cdx-button--weight-quiet mw-interlanguage-selector" id="p-lang-btn-sticky-header" tabindex="-1" data-event-name="ui.dropdown-p-lang-btn-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-language mw-ui-icon-wikimedia-wikimedia-language"></span> <span>67 languages</span> </button> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive" id="ca-addsection-sticky-header" tabindex="-1" data-event-name="addsection-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbleAdd-progressive mw-ui-icon-wikimedia-speechBubbleAdd-progressive"></span> <span>Add topic</span> </a> </div> <div class="vector-sticky-header-icon-end"> <div class="vector-user-links"> </div> </div> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-b766959bd-fzwz8","wgBackendResponseTime":149,"wgPageParseReport":{"limitreport":{"cputime":"1.253","walltime":"1.522","ppvisitednodes":{"value":8390,"limit":1000000},"postexpandincludesize":{"value":287615,"limit":2097152},"templateargumentsize":{"value":7323,"limit":2097152},"expansiondepth":{"value":17,"limit":100},"expensivefunctioncount":{"value":12,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":349784,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 1218.836 1 -total"," 37.49% 456.914 2 Template:Reflist"," 27.50% 335.124 57 Template:Cite_journal"," 10.30% 125.527 1 Template:General_relativity_sidebar"," 10.12% 123.390 1 Template:Sidebar_with_collapsible_lists"," 7.47% 90.988 1 Template:Short_description"," 7.40% 90.160 3 Template:Cite_news"," 5.06% 61.654 2 Template:Pagetype"," 4.77% 58.184 4 Template:Fix"," 4.17% 50.782 1 Template:Commons_category"]},"scribunto":{"limitreport-timeusage":{"value":"0.768","limit":"10.000"},"limitreport-memusage":{"value":9328701,"limit":52428800},"limitreport-logs":"table#1 {\n [\"size\"] = \"tiny\",\n}\n"},"cachereport":{"origin":"mw-api-int.codfw.main-5b65fffc7d-f5css","timestamp":"20250217034538","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Wormhole","url":"https:\/\/en.wikipedia.org\/wiki\/Wormhole","sameAs":"http:\/\/www.wikidata.org\/entity\/Q7544","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q7544","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2001-12-24T10:04:52Z","dateModified":"2025-02-17T03:45:27Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/b\/bc\/Einstein-rosen-bridge-model.png","headline":"hypothetical topological feature of spacetime"}</script> </body> </html>