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<span>History</span> </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Approximate_Newtonian_description" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Approximate_Newtonian_description"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Approximate Newtonian description</span> </div> </a> <ul id="toc-Approximate_Newtonian_description-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Explanation_in_terms_of_spacetime_curvature" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Explanation_in_terms_of_spacetime_curvature"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Explanation in terms of spacetime curvature</span> </div> </a> <ul id="toc-Explanation_in_terms_of_spacetime_curvature-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Search_for_gravitational_lenses" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Search_for_gravitational_lenses"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Search for gravitational lenses</span> </div> </a> <ul id="toc-Search_for_gravitational_lenses-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Solar_gravitational_lens" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Solar_gravitational_lens"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Solar gravitational lens</span> </div> </a> <ul id="toc-Solar_gravitational_lens-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Measuring_weak_lensing" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Measuring_weak_lensing"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Measuring weak lensing</span> </div> </a> <ul id="toc-Measuring_weak_lensing-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Gallery" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Gallery"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Gallery</span> </div> </a> <ul id="toc-Gallery-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">9</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Historical_papers_and_references" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Historical_papers_and_references"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Historical papers and references</span> </div> </a> <ul id="toc-Historical_papers_and_references-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">11</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </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">12</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" > <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">Gravitational lens</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 63 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-63" 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">63 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/Gravitasielens" title="Gravitasielens – Afrikaans" lang="af" hreflang="af" data-title="Gravitasielens" 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%B9%D8%AF%D8%B3%D8%A9_%D8%A7%D9%84%D8%AC%D8%A7%D8%B0%D8%A8%D9%8A%D8%A9" title="عدسة الجاذبية – Arabic" lang="ar" hreflang="ar" data-title="عدسة الجاذبية" 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/Lente_gravitacional" title="Lente gravitacional – Asturian" lang="ast" hreflang="ast" data-title="Lente gravitacional" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AE%E0%A6%B9%E0%A6%BE%E0%A6%95%E0%A6%B0%E0%A7%8D%E0%A6%B7%E0%A7%80%E0%A6%AF%E0%A6%BC_%E0%A6%AA%E0%A6%B0%E0%A6%95%E0%A6%B2%E0%A6%BE" title="মহাকর্ষীয় পরকলা – Bangla" lang="bn" hreflang="bn" data-title="মহাকর্ষীয় পরকলা" 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%93%D1%80%D0%B0%D0%B2%D1%96%D1%82%D0%B0%D1%86%D1%8B%D0%B9%D0%BD%D0%B0%D1%8F_%D0%BB%D1%96%D0%BD%D0%B7%D0%B0" title="Гравітацыйная лінза – Belarusian" lang="be" hreflang="be" data-title="Гравітацыйная лінза" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%93%D1%80%D0%B0%D0%B2%D0%B8%D1%82%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%BD%D0%B0_%D0%BB%D0%B5%D1%89%D0%B0" title="Гравитационна леща – Bulgarian" lang="bg" hreflang="bg" data-title="Гравитационна леща" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Ferenn_c%27hravitadurel" title="Ferenn c'hravitadurel – Breton" lang="br" hreflang="br" data-title="Ferenn c'hravitadurel" data-language-autonym="Brezhoneg" data-language-local-name="Breton" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Lent_gravitat%C3%B2ria" title="Lent gravitatòria – Catalan" lang="ca" hreflang="ca" data-title="Lent gravitatòria" 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%93%D1%80%D0%B0%D0%B2%D0%B8%D1%82%D0%B0%D1%86%D0%B8%D0%BB%D0%BB%D0%B5_%D0%BB%D0%B8%D0%BD%D0%B7%D0%B0" title="Гравитацилле линза – Chuvash" lang="cv" hreflang="cv" data-title="Гравитацилле линза" 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/Gravita%C4%8Dn%C3%AD_%C4%8Do%C4%8Dka" title="Gravitační čočka – Czech" lang="cs" hreflang="cs" data-title="Gravitační čočka" 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/Gravitationslinseeffekt" title="Gravitationslinseeffekt – Danish" lang="da" hreflang="da" data-title="Gravitationslinseeffekt" 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/Gravitationslinseneffekt" title="Gravitationslinseneffekt – German" lang="de" hreflang="de" data-title="Gravitationslinseneffekt" 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/Gravitatsioonil%C3%A4%C3%A4ts" title="Gravitatsioonilääts – Estonian" lang="et" hreflang="et" data-title="Gravitatsioonilääts" 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%92%CE%B1%CF%81%CF%85%CF%84%CE%B9%CE%BA%CF%8C%CF%82_%CF%86%CE%B1%CE%BA%CF%8C%CF%82" title="Βαρυτικός φακός – Greek" lang="el" hreflang="el" data-title="Βαρυτικός φακός" 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/Lente_gravitatoria" title="Lente gravitatoria – Spanish" lang="es" hreflang="es" data-title="Lente gravitatoria" 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/Gravita_lenso" title="Gravita lenso – Esperanto" lang="eo" hreflang="eo" data-title="Gravita lenso" 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/Grabitazio-leiar" title="Grabitazio-leiar – Basque" lang="eu" hreflang="eu" data-title="Grabitazio-leiar" 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/%D9%87%D9%85%DA%AF%D8%B1%D8%A7%DB%8C%DB%8C_%DA%AF%D8%B1%D8%A7%D9%86%D8%B4%DB%8C" title="همگرایی گرانشی – Persian" lang="fa" hreflang="fa" data-title="همگرایی گرانشی" 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/Lentille_gravitationnelle" title="Lentille gravitationnelle – French" lang="fr" hreflang="fr" data-title="Lentille gravitationnelle" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Lionsa_imtharraingteach" title="Lionsa imtharraingteach – Irish" lang="ga" hreflang="ga" data-title="Lionsa imtharraingteach" 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/Lente_gravitacional" title="Lente gravitacional – Galician" lang="gl" hreflang="gl" data-title="Lente gravitacional" 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%A4%91%EB%A0%A5%EB%A0%8C%EC%A6%88" title="중력렌즈 – Korean" lang="ko" hreflang="ko" data-title="중력렌즈" 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/%D4%B3%D6%80%D5%A1%D5%BE%D5%AB%D5%BF%D5%A1%D6%81%D5%AB%D5%B8%D5%B6_%D5%B8%D5%BD%D5%BA%D5%B6%D5%B5%D5%A1%D5%AF" title="Գրավիտացիոն ոսպնյակ – Armenian" lang="hy" hreflang="hy" data-title="Գրավիտացիոն ոսպնյակ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%97%E0%A5%81%E0%A4%B0%E0%A5%81%E0%A4%A4%E0%A5%8D%E0%A4%B5%E0%A4%BE%E0%A4%95%E0%A4%B0%E0%A5%8D%E0%A4%B7%E0%A4%95_%E0%A4%B2%E0%A5%87%E0%A4%82%E0%A4%B8" title="गुरुत्वाकर्षक लेंस – Hindi" lang="hi" hreflang="hi" data-title="गुरुत्वाकर्षक लेंस" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Gravitacijske_le%C4%87e" title="Gravitacijske leće – Croatian" lang="hr" hreflang="hr" data-title="Gravitacijske leće" 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/Anya_nd%E1%BB%8Dda" title="Anya ndọda – Igbo" lang="ig" hreflang="ig" data-title="Anya ndọda" 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/Lensa_gravitasi" title="Lensa gravitasi – Indonesian" lang="id" hreflang="id" data-title="Lensa gravitasi" 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-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Lente_gravitazionale" title="Lente gravitazionale – Italian" lang="it" hreflang="it" data-title="Lente gravitazionale" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A2%D7%99%D7%93%D7%95%D7%A9_%D7%9B%D7%91%D7%99%D7%93%D7%AA%D7%99" title="עידוש כבידתי – Hebrew" lang="he" hreflang="he" data-title="עידוש כבידתי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%92%E1%83%A0%E1%83%90%E1%83%95%E1%83%98%E1%83%A2%E1%83%90%E1%83%AA%E1%83%98%E1%83%A3%E1%83%9A%E1%83%98_%E1%83%9A%E1%83%98%E1%83%9C%E1%83%96%E1%83%98%E1%83%A0%E1%83%94%E1%83%91%E1%83%90" title="გრავიტაციული ლინზირება – Georgian" lang="ka" hreflang="ka" data-title="გრავიტაციული ლინზირება" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Lenzi_ya_uvutano" title="Lenzi ya uvutano – Swahili" lang="sw" hreflang="sw" data-title="Lenzi ya uvutano" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Gravit%C4%81cijas_l%C4%93ca" title="Gravitācijas lēca – Latvian" lang="lv" hreflang="lv" data-title="Gravitācijas lēca" 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/Gravitacinis_l%C4%99%C5%A1is" title="Gravitacinis lęšis – Lithuanian" lang="lt" hreflang="lt" data-title="Gravitacinis lęšis" 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/Gravit%C3%A1ci%C3%B3s_lencse" title="Gravitációs lencse – Hungarian" lang="hu" hreflang="hu" data-title="Gravitációs lencse" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%97%E0%B5%8D%E0%B4%B0%E0%B4%BE%E0%B4%B5%E0%B4%BF%E0%B4%B1%E0%B5%8D%E0%B4%B1%E0%B5%87%E0%B4%B7%E0%B4%A8%E0%B5%BD_%E0%B4%B2%E0%B5%86%E0%B5%BB%E0%B4%B8%E0%B5%8D" title="ഗ്രാവിറ്റേഷനൽ ലെൻസ് – Malayalam" lang="ml" hreflang="ml" data-title="ഗ്രാവിറ്റേഷനൽ ലെൻസ്" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Zwaartekrachtlens" title="Zwaartekrachtlens – Dutch" lang="nl" hreflang="nl" data-title="Zwaartekrachtlens" 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/%E9%87%8D%E5%8A%9B%E3%83%AC%E3%83%B3%E3%82%BA" title="重力レンズ – Japanese" lang="ja" hreflang="ja" data-title="重力レンズ" 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/Gravitasjonslinse" title="Gravitasjonslinse – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Gravitasjonslinse" 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/Gravitasjonslinse" title="Gravitasjonslinse – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Gravitasjonslinse" 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-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Lentilha_gravitacionala" title="Lentilha gravitacionala – Occitan" lang="oc" hreflang="oc" data-title="Lentilha gravitacionala" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Gravitatsion_linzalar" title="Gravitatsion linzalar – Uzbek" lang="uz" hreflang="uz" data-title="Gravitatsion linzalar" 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-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%97%E0%A8%B0%E0%A9%88%E0%A8%B5%E0%A9%80%E0%A8%9F%E0%A9%87%E0%A8%B8%E0%A8%BC%E0%A8%A8%E0%A8%B2_%E0%A8%B2%E0%A9%88%E0%A9%B1%E0%A8%A8%E0%A8%9C%E0%A8%BC%E0%A8%BF%E0%A9%B0%E0%A8%97" title="ਗਰੈਵੀਟੇਸ਼ਨਲ ਲੈੱਨਜ਼ਿੰਗ – Punjabi" lang="pa" hreflang="pa" data-title="ਗਰੈਵੀਟੇਸ਼ਨਲ ਲੈੱਨਜ਼ਿੰਗ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Soczewkowanie_grawitacyjne" title="Soczewkowanie grawitacyjne – Polish" lang="pl" hreflang="pl" data-title="Soczewkowanie grawitacyjne" 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/Lente_gravitacional" title="Lente gravitacional – Portuguese" lang="pt" hreflang="pt" data-title="Lente gravitacional" 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/Lentil%C4%83_gravita%C8%9Bional%C4%83" title="Lentilă gravitațională – Romanian" lang="ro" hreflang="ro" data-title="Lentilă gravitațională" 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%93%D1%80%D0%B0%D0%B2%D0%B8%D1%82%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%BD%D0%B0%D1%8F_%D0%BB%D0%B8%D0%BD%D0%B7%D0%B0" title="Гравитационная линза – Russian" lang="ru" hreflang="ru" data-title="Гравитационная линза" 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/Gravitational_lensing" title="Gravitational lensing – Simple English" lang="en-simple" hreflang="en-simple" data-title="Gravitational lensing" 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/Gravita%C4%8Dn%C3%A1_%C5%A1o%C5%A1ovka" title="Gravitačná šošovka – Slovak" lang="sk" hreflang="sk" data-title="Gravitačná šošovka" 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/Gravitacijska_le%C4%8Da" title="Gravitacijska leča – Slovenian" lang="sl" hreflang="sl" data-title="Gravitacijska leča" 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%93%D1%80%D0%B0%D0%B2%D0%B8%D1%82%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%BE_%D1%81%D0%BE%D1%87%D0%B8%D0%B2%D0%BE" title="Гравитационо сочиво – Serbian" lang="sr" hreflang="sr" data-title="Гравитационо сочиво" 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/Gravitacijske_le%C4%87e" title="Gravitacijske leće – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Gravitacijske leće" 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/Gravitaatiolinssi" title="Gravitaatiolinssi – Finnish" lang="fi" hreflang="fi" data-title="Gravitaatiolinssi" 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/Gravitationslins" title="Gravitationslins – Swedish" lang="sv" hreflang="sv" data-title="Gravitationslins" 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%88%E0%AE%B0%E0%AF%8D%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%81_%E0%AE%B5%E0%AE%BF%E0%AE%B2%E0%AF%8D%E0%AE%B2%E0%AF%88" title="ஈர்ப்பு வில்லை – Tamil" lang="ta" hreflang="ta" data-title="ஈர்ப்பு வில்லை" 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%93%D1%80%D0%B0%D0%B2%D0%B8%D1%82%D0%B0%D1%86%D0%B8%D0%BE%D0%BD_%D0%BB%D0%B8%D0%BD%D0%B7%D0%B0" title="Гравитацион линза – Tatar" lang="tt" hreflang="tt" data-title="Гравитацион линза" 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%B9%80%E0%B8%A5%E0%B8%99%E0%B8%AA%E0%B9%8C%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B9%82%E0%B8%99%E0%B9%89%E0%B8%A1%E0%B8%96%E0%B9%88%E0%B8%A7%E0%B8%87" title="เลนส์ความโน้มถ่วง – Thai" lang="th" hreflang="th" data-title="เลนส์ความโน้มถ่วง" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/K%C3%BCtle%C3%A7ekimsel_merceklenme" title="Kütleçekimsel merceklenme – Turkish" lang="tr" hreflang="tr" data-title="Kütleçekimsel merceklenme" 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%93%D1%80%D0%B0%D0%B2%D1%96%D1%82%D0%B0%D1%86%D1%96%D0%B9%D0%BD%D0%B0_%D0%BB%D1%96%D0%BD%D0%B7%D0%B0" title="Гравітаційна лінза – Ukrainian" lang="uk" hreflang="uk" data-title="Гравітаційна лінза" 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/%D8%AB%D9%82%D9%84%DB%8C_%D8%B9%D8%AF%D8%B3%DB%81" title="ثقلی عدسہ – Urdu" lang="ur" hreflang="ur" data-title="ثقلی عدسہ" 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/Th%E1%BA%A5u_k%C3%ADnh_h%E1%BA%A5p_d%E1%BA%ABn" title="Thấu kính hấp dẫn – Vietnamese" lang="vi" hreflang="vi" data-title="Thấu kính hấp dẫn" 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/%E5%BC%95%E5%8A%9B%E9%80%8F%E9%95%9C%E6%95%88%E5%BA%94" title="引力透镜效应 – Wu" lang="wuu" hreflang="wuu" data-title="引力透镜效应" 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/%E5%BC%95%E5%8A%9B%E9%80%8F%E9%8F%A1" title="引力透鏡 – Cantonese" lang="yue" hreflang="yue" data-title="引力透鏡" 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/%E5%BC%95%E5%8A%9B%E9%80%8F%E9%95%9C%E6%95%88%E5%BA%94" title="引力透镜效应 – Chinese" lang="zh" hreflang="zh" data-title="引力透镜效应" 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 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.sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle">Part of a series of articles about</td></tr><tr><th class="sidebar-title-with-pretitle"><a class="mw-selflink selflink">Gravitational lensing</a></th></tr><tr><td class="sidebar-image"><span typeof="mw:File/Frameless"><a href="/wiki/File:A_Horseshoe_Einstein_Ring_from_Hubble.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/A_Horseshoe_Einstein_Ring_from_Hubble.JPG/250px-A_Horseshoe_Einstein_Ring_from_Hubble.JPG" decoding="async" width="250" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/A_Horseshoe_Einstein_Ring_from_Hubble.JPG/375px-A_Horseshoe_Einstein_Ring_from_Hubble.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/11/A_Horseshoe_Einstein_Ring_from_Hubble.JPG/500px-A_Horseshoe_Einstein_Ring_from_Hubble.JPG 2x" data-file-width="1014" data-file-height="670" /></a></span></td></tr><tr><td class="sidebar-content"> <a href="/wiki/Einstein_ring" title="Einstein ring">Einstein ring</a><br /><a href="/wiki/Gravitational_lensing_formalism" title="Gravitational lensing formalism">Formalism</a><br /><a href="/wiki/Strong_gravitational_lensing" title="Strong gravitational lensing">Strong lensing</a><br /><a href="/wiki/Gravitational_microlensing" title="Gravitational microlensing">Microlensing</a><br /><a href="/wiki/Weak_gravitational_lensing" title="Weak gravitational lensing">Weak lensing</a></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Strong lens systems</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Abell_1689" title="Abell 1689">Abell 1689</a></li> <li><a href="/wiki/Abell_2218" title="Abell 2218">Abell 2218</a><br /><a href="/wiki/CL0024%2B17" title="CL0024+17">CL0024+17</a></li> <li><a href="/wiki/Bullet_Cluster" title="Bullet Cluster">Bullet Cluster</a><br /><a href="/wiki/Einstein_Cross" title="Einstein Cross">QSO2237+0305</a></li> <li><a href="/wiki/SDSSJ0946%2B1006" title="SDSSJ0946+1006">SDSSJ0946+1006</a><br /><a href="/wiki/B1359%2B154" class="mw-redirect" title="B1359+154">B1359+154</a></li> <li><a href="/wiki/Twin_Quasar" title="Twin Quasar">QSO 0957+561</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="color: var(--color-base)">Surveys</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li>Strong: <a href="/w/index.php?title=Cosmic_Lens_All-Sky_Survey&action=edit&redlink=1" class="new" title="Cosmic Lens All-Sky Survey (page does not exist)">CLASS</a></li> <li><a href="/w/index.php?title=SLACS&action=edit&redlink=1" class="new" title="SLACS (page does not exist)">SLACS</a> <ul><li><a href="/wiki/Sloan_Digital_Sky_Survey" title="Sloan Digital Sky Survey">SDSS</a></li></ul></li></ul> <ul><li>Micro: <a href="/wiki/Optical_Gravitational_Lensing_Experiment" title="Optical Gravitational Lensing Experiment">OGLE</a></li> <li><a href="/wiki/Gaia_(spacecraft)" title="Gaia (spacecraft)">Gaia</a><br /> Weak: <a href="/wiki/Deep_Lens_Survey" title="Deep Lens Survey">DLS</a></li> <li><a href="/wiki/Pan-STARRS" title="Pan-STARRS">Pan-STARRS</a></li> <li><a href="/wiki/CFHT" class="mw-redirect" title="CFHT">CFHTLS</a></li> <li><a href="/wiki/Dark_Energy_Survey" title="Dark Energy Survey">DES</a></li> <li><a href="/wiki/Large_Synoptic_Survey_Telescope" class="mw-redirect" title="Large Synoptic Survey Telescope">LSST</a></li> <li><a href="/wiki/Supernova/Acceleration_Probe" class="mw-redirect" title="Supernova/Acceleration Probe">SNAP</a></li> <li><a href="/wiki/Dark_Energy_Space_Telescope" class="mw-redirect" title="Dark Energy Space Telescope">DESTINY</a></li></ul></div></div></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 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//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 ); 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 class="mw-selflink selflink">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 href="/wiki/Wormhole" title="Wormhole">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 ); 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 href="/wiki/Wormhole" title="Wormhole">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"><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: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> <figure typeof="mw:File/Thumb"><a href="/wiki/File:A_remote_light_source_passing_behind_a_gravitational_lens.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/A_remote_light_source_passing_behind_a_gravitational_lens.gif/231px-A_remote_light_source_passing_behind_a_gravitational_lens.gif" decoding="async" width="231" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/0/06/A_remote_light_source_passing_behind_a_gravitational_lens.gif 1.5x" data-file-width="308" data-file-height="160" /></a><figcaption>A light source passes behind a gravitational lens (invisible point mass placed in the center of the image). The aqua circle is the light source as it would be seen if there were no lens, while white spots are the multiple images of the source (see <a href="/wiki/Einstein_ring" title="Einstein ring">Einstein ring</a>).</figcaption></figure> <p>A <b>gravitational lens</b> is matter, such as a <a href="/wiki/Galaxy_cluster" title="Galaxy cluster">cluster of galaxies</a> or a <a href="/wiki/Point_particle" title="Point particle">point particle</a>, that bends light from a distant source as it travels toward an observer. The amount of <b>gravitational lensing</b> is described by <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a>'s <a href="/wiki/General_relativity" title="General relativity">general theory of relativity</a>.<sup id="cite_ref-NYT-20150305-video_1-0" class="reference"><a href="#cite_note-NYT-20150305-video-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-NYT-20150305_2-0" class="reference"><a href="#cite_note-NYT-20150305-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> If light is treated as <a href="/wiki/Corpuscular_theory_of_light" title="Corpuscular theory of light">corpuscles</a> travelling at the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a>, <a href="/wiki/Newtonian_physics" class="mw-redirect" title="Newtonian physics">Newtonian physics</a> also predicts the bending of light, but only half of that predicted by general relativity.<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><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><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><p><a href="/wiki/Orest_Khvolson" title="Orest Khvolson">Orest Khvolson</a> (1924)<sup id="cite_ref-Early_History_of_Gravitational_Lensing_7-0" class="reference"><a href="#cite_note-Early_History_of_Gravitational_Lensing-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> and <a href="/w/index.php?title=Frantisek_Link&action=edit&redlink=1" class="new" title="Frantisek Link (page does not exist)">Frantisek Link</a> (1936)<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> are generally credited with being the first to discuss the effect in print, but it is more commonly associated with Einstein, who made unpublished calculations on it in 1912<sup id="cite_ref-origin_of_the_idea_9-0" class="reference"><a href="#cite_note-origin_of_the_idea-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> and published an article on the subject in 1936.<sup id="cite_ref-:0_10-0" class="reference"><a href="#cite_note-:0-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>In 1937, <a href="/wiki/Fritz_Zwicky" title="Fritz Zwicky">Fritz Zwicky</a> posited that galaxy clusters could act as gravitational lenses, a claim confirmed in 1979 by observation of the <a href="/wiki/Twin_QSO" class="mw-redirect" title="Twin QSO">Twin QSO</a> SBS 0957+561. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Description">Description</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gravitational_lens&action=edit&section=1" title="Edit section: Description"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><video id="mwe_player_0" poster="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Artist%27s_impression_of_gravitational_lensing_of_a_distant_merger.ogv/220px--Artist%27s_impression_of_gravitational_lensing_of_a_distant_merger.ogv.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="124" data-durationhint="31" data-mwtitle="Artist's_impression_of_gravitational_lensing_of_a_distant_merger.ogv" data-mwprovider="wikimediacommons" resource="/wiki/File:Artist%27s_impression_of_gravitational_lensing_of_a_distant_merger.ogv"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/99/Artist%27s_impression_of_gravitational_lensing_of_a_distant_merger.ogv/Artist%27s_impression_of_gravitational_lensing_of_a_distant_merger.ogv.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/99/Artist%27s_impression_of_gravitational_lensing_of_a_distant_merger.ogv/Artist%27s_impression_of_gravitational_lensing_of_a_distant_merger.ogv.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/99/Artist%27s_impression_of_gravitational_lensing_of_a_distant_merger.ogv/Artist%27s_impression_of_gravitational_lensing_of_a_distant_merger.ogv.1080p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="1080p.vp9.webm" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/9/99/Artist%27s_impression_of_gravitational_lensing_of_a_distant_merger.ogv" type="video/ogg; codecs="theora"" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/99/Artist%27s_impression_of_gravitational_lensing_of_a_distant_merger.ogv/Artist%27s_impression_of_gravitational_lensing_of_a_distant_merger.ogv.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="256" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/99/Artist%27s_impression_of_gravitational_lensing_of_a_distant_merger.ogv/Artist%27s_impression_of_gravitational_lensing_of_a_distant_merger.ogv.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/99/Artist%27s_impression_of_gravitational_lensing_of_a_distant_merger.ogv/Artist%27s_impression_of_gravitational_lensing_of_a_distant_merger.ogv.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/99/Artist%27s_impression_of_gravitational_lensing_of_a_distant_merger.ogv/Artist%27s_impression_of_gravitational_lensing_of_a_distant_merger.ogv.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span><figcaption>Gravitational lensing – intervening galaxy modifies appearance of a galaxy far behind it (video; artist's concept).</figcaption></figure> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><span><video id="mwe_player_1" poster="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_-vid-.webm/220px--Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_-vid-.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="124" data-durationhint="26" data-mwtitle="Gravitational_lensing_of_distant_star-forming_galaxies_(schematic)_-vid-.webm" data-mwprovider="wikimediacommons" resource="/wiki/File:Gravitational_lensing_of_distant_star-forming_galaxies_(schematic)_-vid-.webm"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/02/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_-vid-.webm/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_-vid-.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/02/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_-vid-.webm/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_-vid-.webm.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/02/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_-vid-.webm/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_-vid-.webm.1080p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="1080p.vp9.webm" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/0/02/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_-vid-.webm" type="video/webm; codecs="vp8"" data-width="3840" data-height="2160" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/02/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_-vid-.webm/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_-vid-.webm.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="256" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/02/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_-vid-.webm/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_-vid-.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/02/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_-vid-.webm/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_-vid-.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/02/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_-vid-.webm/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_-vid-.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span><figcaption>This schematic image shows how light from a distant galaxy is distorted by the gravitational effects of a foreground galaxy, which acts like a lens and makes the distant source appear distorted, but magnified, forming characteristic rings of light, known as Einstein rings.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><video id="mwe_player_2" poster="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_2.webm/220px--Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_2.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="124" data-durationhint="28" data-mwtitle="Gravitational_lensing_of_distant_star-forming_galaxies_(schematic)_2.webm" data-mwprovider="wikimediacommons" resource="/wiki/File:Gravitational_lensing_of_distant_star-forming_galaxies_(schematic)_2.webm"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e7/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_2.webm/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_2.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e7/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_2.webm/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_2.webm.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e7/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_2.webm/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_2.webm.1080p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="1080p.vp9.webm" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/e/e7/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_2.webm" type="video/webm; codecs="vp8"" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e7/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_2.webm/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_2.webm.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="256" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e7/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_2.webm/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_2.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e7/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_2.webm/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_2.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e7/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_2.webm/Gravitational_lensing_of_distant_star-forming_galaxies_%28schematic%29_2.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span><figcaption>An analysis of the distortion of SDP.81 caused by this effect has revealed star-forming clumps of matter.</figcaption></figure> <p>Unlike an <a href="/wiki/Lens_(optics)" class="mw-redirect" title="Lens (optics)">optical lens</a>, a point-like gravitational lens produces a maximum deflection of light that passes closest to its center, and a minimum deflection of light that travels furthest from its center. Consequently, a gravitational lens has no single <a href="/wiki/Focus_(optics)" title="Focus (optics)">focal point</a>, but a focal line. The term "lens" in the context of gravitational light deflection was first used by O. J. Lodge, who remarked that it is "not permissible to say that the solar gravitational field acts like a lens, for it has no focal length".<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> If the (light) source, the massive lensing object, and the observer lie in a straight line, the original light source will appear as a ring around the massive lensing object (provided the lens has circular symmetry). If there is any misalignment, the observer will see an arc segment instead. </p><p>This phenomenon was first mentioned in 1924 by the <a href="/wiki/St._Petersburg" class="mw-redirect" title="St. Petersburg">St. Petersburg</a> physicist <a href="/wiki/Orest_Khvolson" title="Orest Khvolson">Orest Khvolson</a>,<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> and quantified by <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> in 1936. It is usually referred to in the literature as an <a href="/wiki/Einstein_ring" title="Einstein ring">Einstein ring</a>, since Khvolson did not concern himself with the flux or radius of the ring image. More commonly, where the lensing mass is complex (such as a <a href="/wiki/Galaxy_group" title="Galaxy group">galaxy group</a> or <a href="/wiki/Galaxy_cluster" title="Galaxy cluster">cluster</a>) and does not cause a spherical distortion of spacetime, the source will resemble partial arcs scattered around the lens. The observer may then see multiple distorted images of the same source; the number and shape of these depending upon the relative positions of the source, lens, and observer, and the shape of the gravitational well of the lensing object. </p><p>There are three classes of gravitational lensing:<sup id="cite_ref-Schneider,_Peter;_Ehlers,_Jürgen;_Falco,_Emilio_E._1992_13-0" class="reference"><a href="#cite_note-Schneider,_Peter;_Ehlers,_Jürgen;_Falco,_Emilio_E._1992-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 399–401">: 399–401 </span></sup><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <dl><dt><a href="/wiki/Strong_gravitational_lensing" title="Strong gravitational lensing">Strong lensing</a></dt> <dd>Where there are easily visible distortions such as the formation of <a href="/wiki/Einstein_ring" title="Einstein ring">Einstein rings</a>, arcs, and multiple images. Despite being considered "strong", the effect is in general relatively small, such that even a galaxy with a mass more than 100 billion times <a href="/wiki/Solar_mass" title="Solar mass">that of the Sun</a> will produce multiple images separated by only a few <a href="/wiki/Arcsecond" class="mw-redirect" title="Arcsecond">arcseconds</a>. <a href="/wiki/Galaxy_cluster" title="Galaxy cluster">Galaxy clusters</a> can produce separations of several arcminutes. In both cases the galaxies and sources are quite distant, many hundreds of <a href="/wiki/Megaparsec" class="mw-redirect" title="Megaparsec">megaparsecs</a> away from our Galaxy.</dd> <dt><a href="/wiki/Weak_gravitational_lensing" title="Weak gravitational lensing">Weak lensing</a></dt> <dd>Where the distortions of background sources are much smaller and can only be detected by analyzing large numbers of sources in a statistical way to find coherent distortions of only a few percent. The lensing shows up statistically as a preferred stretching of the background objects perpendicular to the direction to the centre of the lens. By measuring the shapes and orientations of large numbers of distant galaxies, their orientations can be averaged to measure the <a href="/wiki/Shear_matrix" class="mw-redirect" title="Shear matrix">shear</a> of the lensing field in any region. This, in turn, can be used to reconstruct the mass distribution in the area: in particular, the background distribution of <a href="/wiki/Dark_matter" title="Dark matter">dark matter</a> can be reconstructed. Since galaxies are intrinsically elliptical and the weak gravitational lensing signal is small, a very large number of galaxies must be used in these surveys. These weak lensing surveys must carefully avoid a number of important sources of <a href="/wiki/Systematic_error" class="mw-redirect" title="Systematic error">systematic error</a>: the intrinsic shape of galaxies, the tendency of a camera's <a href="/wiki/Point_spread_function" title="Point spread function">point spread function</a> to distort the shape of a galaxy and the tendency of <a href="/wiki/Atmospheric_seeing" class="mw-redirect" title="Atmospheric seeing">atmospheric seeing</a> to distort images must be understood and carefully accounted for. The results of these surveys are important for cosmological parameter estimation, to better understand and improve upon the <a href="/wiki/Lambda-CDM_model" title="Lambda-CDM model">Lambda-CDM model</a>, and to provide a consistency check on other cosmological observations. They may also provide an important future constraint on <a href="/wiki/Dark_energy" title="Dark energy">dark energy</a>.</dd> <dt><a href="/wiki/Gravitational_microlensing" title="Gravitational microlensing">Microlensing</a></dt> <dd>Where no distortion in shape can be seen but the amount of light received from a background object changes in time. The lensing object may be stars in the <a href="/wiki/Milky_Way_Galaxy" class="mw-redirect" title="Milky Way Galaxy">Milky Way</a> in one typical case, with the background source being stars in a remote galaxy, or, in another case, an even more distant <a href="/wiki/Quasar" title="Quasar">quasar</a>. In extreme cases, a star in a distant galaxy can act as a microlens and magnify another star much farther away. The first example of this was the star <a href="/wiki/MACS_J1149_Lensed_Star_1" title="MACS J1149 Lensed Star 1">MACS J1149 Lensed Star 1</a> (also known as Icarus), thanks to the boost in flux due to the microlensing effect.</dd></dl> <p>Gravitational lenses act equally on all kinds of <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a>, not just visible light, and also in non-electromagnetic radiation, like gravitational waves. Weak lensing effects are being studied for the <a href="/wiki/Cosmic_microwave_background" title="Cosmic microwave background">cosmic microwave background</a> as well as <a href="/wiki/Galaxy_survey" class="mw-redirect" title="Galaxy survey">galaxy surveys</a>. Strong lenses have been observed in <a href="/wiki/Radio" title="Radio">radio</a> and <a href="/wiki/X-ray" title="X-ray">x-ray</a> regimes as well. If a strong lens produces multiple images, there will be a relative time delay between two paths: that is, in one image the lensed object will be observed before the other image. </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gravitational_lens&action=edit&section=2" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:1919_eclipse_negative.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/1919_eclipse_negative.jpg/150px-1919_eclipse_negative.jpg" decoding="async" width="150" height="193" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/1919_eclipse_negative.jpg/225px-1919_eclipse_negative.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/da/1919_eclipse_negative.jpg/300px-1919_eclipse_negative.jpg 2x" data-file-width="700" data-file-height="899" /></a><figcaption>One of <a href="/wiki/Sir_Arthur_Eddington" class="mw-redirect" title="Sir Arthur Eddington">Eddington</a>'s photographs of the 1919 <a href="/wiki/Solar_eclipse" title="Solar eclipse">solar eclipse</a> experiment, presented in his 1920 paper announcing its success</figcaption></figure> <p><a href="/wiki/Henry_Cavendish" title="Henry Cavendish">Henry Cavendish</a> in 1784 (in an unpublished manuscript) and <a href="/wiki/Johann_Georg_von_Soldner" title="Johann Georg von Soldner">Johann Georg von Soldner</a> in 1801 (published in 1804) had pointed out that Newtonian gravity predicts that starlight will bend around a massive object<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> as had already been supposed by <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> in 1704 in his <i><a href="/wiki/The_Queries" class="mw-redirect" title="The Queries">Queries</a></i> No.1 in his book <i><a href="/wiki/Opticks" title="Opticks">Opticks</a></i>.<sup id="cite_ref-Opticks_16-0" class="reference"><a href="#cite_note-Opticks-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> The same value as Soldner's was calculated by Einstein in 1911 based on the <a href="/wiki/Equivalence_principle" title="Equivalence principle">equivalence principle</a> alone.<sup id="cite_ref-Schneider,_Peter;_Ehlers,_Jürgen;_Falco,_Emilio_E._1992_13-1" class="reference"><a href="#cite_note-Schneider,_Peter;_Ehlers,_Jürgen;_Falco,_Emilio_E._1992-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 3">: 3 </span></sup> However, Einstein noted in 1915, in the process of completing general relativity, that his (and thus Soldner's) 1911-result is only half of the correct value. Einstein became the first to calculate the correct value for light bending.<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> </p><p>The first observation of light deflection was performed by noting the change in position of <a href="/wiki/Star" title="Star">stars</a> as they passed near the Sun on the <a href="/wiki/Celestial_sphere" title="Celestial sphere">celestial sphere</a>. The observations were performed in 1919 by <a href="/wiki/Sir_Arthur_Eddington" class="mw-redirect" title="Sir Arthur Eddington">Arthur Eddington</a>, <a href="/wiki/Frank_Watson_Dyson" title="Frank Watson Dyson">Frank Watson Dyson</a>, and their collaborators during the <a href="/wiki/Solar_eclipse_of_May_29,_1919" title="Solar eclipse of May 29, 1919">total solar eclipse on May 29</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> The <a href="/wiki/Solar_eclipse" title="Solar eclipse">solar eclipse</a> allowed the stars near the Sun to be observed. Observations were made simultaneously in the cities of <a href="/wiki/Sobral,_Cear%C3%A1" title="Sobral, Ceará">Sobral, Ceará</a>, Brazil and in <a href="/wiki/S%C3%A3o_Tom%C3%A9_and_Pr%C3%ADncipe" title="São Tomé and Príncipe">São Tomé and Príncipe</a> on the west coast of Africa.<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> The observations demonstrated that the light from <a href="/wiki/Star" title="Star">stars</a> passing close to the <a href="/wiki/Sun" title="Sun">Sun</a> was slightly bent, so that stars appeared slightly out of position.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Gravitational_lens-full.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Gravitational_lens-full.jpg/220px-Gravitational_lens-full.jpg" decoding="async" width="220" height="166" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Gravitational_lens-full.jpg/330px-Gravitational_lens-full.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/02/Gravitational_lens-full.jpg/440px-Gravitational_lens-full.jpg 2x" data-file-width="702" data-file-height="531" /></a><figcaption>Bending light around a massive object from a distant source. The orange arrows show the apparent position of the background source. The white arrows show the path of the light from the true position of the source.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Einstein_cross.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Einstein_cross.jpg/220px-Einstein_cross.jpg" decoding="async" width="220" height="212" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Einstein_cross.jpg/330px-Einstein_cross.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Einstein_cross.jpg/440px-Einstein_cross.jpg 2x" data-file-width="1915" data-file-height="1849" /></a><figcaption>In the formation known as <a href="/wiki/Einstein%27s_Cross" class="mw-redirect" title="Einstein's Cross">Einstein's Cross</a>, four images of the same distant <a href="/wiki/Quasar" title="Quasar">quasar</a> appear around a foreground galaxy due to strong gravitational lensing.</figcaption></figure> <p>The result was considered spectacular news and made the front page of most major newspapers. It made Einstein and his theory of general relativity world-famous. When asked by his assistant what his reaction would have been if general relativity had not been confirmed by Eddington and Dyson in 1919, Einstein said "Then I would feel sorry for the dear Lord. The theory is correct anyway."<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> In 1912, Einstein had speculated that an observer could see multiple images of a single light source, if the light were deflected around a mass. This effect would make the mass act as a kind of gravitational lens. However, as he only considered the effect of deflection around a single star, he seemed to conclude that the phenomenon was unlikely to be observed for the foreseeable future since the necessary alignments between stars and observer would be highly improbable. Several other physicists speculated about gravitational lensing as well, but all reached the same conclusion that it would be nearly impossible to observe.<sup id="cite_ref-:0_10-1" class="reference"><a href="#cite_note-:0-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>Although Einstein made unpublished calculations on the subject,<sup id="cite_ref-origin_of_the_idea_9-1" class="reference"><a href="#cite_note-origin_of_the_idea-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> the first discussion of the gravitational lens in print was by Khvolson, in a short article discussing the "halo effect" of gravitation when the source, lens, and observer are in near-perfect alignment,<sup id="cite_ref-Early_History_of_Gravitational_Lensing_7-1" class="reference"><a href="#cite_note-Early_History_of_Gravitational_Lensing-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> now referred to as the <a href="/wiki/Einstein_ring" title="Einstein ring">Einstein ring</a>. </p><p>In 1936, after some urging by Rudi W. Mandl, Einstein reluctantly published the short article "Lens-Like Action of a Star By the Deviation of Light In the Gravitational Field" in the journal <i>Science</i>.<sup id="cite_ref-:0_10-2" class="reference"><a href="#cite_note-:0-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>In 1937, <a href="/wiki/Fritz_Zwicky" title="Fritz Zwicky">Fritz Zwicky</a> first considered the case where the newly discovered <a href="/wiki/Galaxy" title="Galaxy">galaxies</a> (which were called 'nebulae' at the time) could act as both source and lens, and that, because of the mass and sizes involved, the effect was much more likely to be observed.<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> </p><p>In 1963 Yu. G. Klimov, S. Liebes, and <a href="/wiki/Sjur_Refsdal" title="Sjur Refsdal">Sjur Refsdal</a> recognized independently that quasars are an ideal light source for the gravitational lens effect.<sup id="cite_ref-Schneider,_Peter;_Kochanek,_Christopher;_Wambsganss,_Joachim_23-0" class="reference"><a href="#cite_note-Schneider,_Peter;_Kochanek,_Christopher;_Wambsganss,_Joachim-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p><p>It was not until 1979 that the first gravitational lens would be discovered. It became known as the "<a href="/wiki/Twin_QSO" class="mw-redirect" title="Twin QSO">Twin QSO</a>" since it initially looked like two identical quasistellar objects. (It is officially named <a href="/wiki/SBS_0957%2B561" class="mw-redirect" title="SBS 0957+561">SBS 0957+561</a>.) This gravitational lens was discovered by <a href="/wiki/Dennis_Walsh" title="Dennis Walsh">Dennis Walsh</a>, Bob Carswell, and <a href="/wiki/Ray_Weymann" title="Ray Weymann">Ray Weymann</a> using the <a href="/wiki/Kitt_Peak_National_Observatory" title="Kitt Peak National Observatory">Kitt Peak National Observatory</a> 2.1 meter <a href="/wiki/Telescope" title="Telescope">telescope</a>.<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> </p><p>In the 1980s, astronomers realized that the combination of CCD imagers and computers would allow the brightness of millions of stars to be measured each night. In a dense field, such as the galactic center or the Magellanic clouds, many microlensing events per year could potentially be found. This led to efforts such as <a href="/wiki/Optical_Gravitational_Lensing_Experiment" title="Optical Gravitational Lensing Experiment">Optical Gravitational Lensing Experiment</a>, or OGLE, that have characterized hundreds of such events, including those of <a href="/wiki/OGLE-2016-BLG-1190Lb" title="OGLE-2016-BLG-1190Lb">OGLE-2016-BLG-1190Lb</a> and <a href="/wiki/OGLE-2016-BLG-1195Lb" title="OGLE-2016-BLG-1195Lb">OGLE-2016-BLG-1195Lb</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Approximate_Newtonian_description">Approximate Newtonian description</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gravitational_lens&action=edit&section=3" title="Edit section: Approximate Newtonian description"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Newton wondered whether light, in the form of corpuscles, would be bent due to gravity. The Newtonian prediction for light deflection refers to the amount of deflection a corpuscle would feel under the effect of gravity, and therefore one should read "Newtonian" in this context as the referring to the following calculations and not a belief that Newton held in the validity of these calculations.<sup id="cite_ref-Meneghetti_25-0" class="reference"><a href="#cite_note-Meneghetti-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p><p>For a gravitational point-mass lens of mass <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}"></span>, a corpuscle of mass <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span> feels a <a href="/wiki/Newton%27s_law_of_universal_gravitation" title="Newton's law of universal gravitation">force</a> </p> <dl><dd><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 {\vec {F}}=-{\frac {GMm}{r^{2}}}{\hat {r}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>G</mi> <mi>M</mi> <mi>m</mi> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}=-{\frac {GMm}{r^{2}}}{\hat {r}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d933492f46a4e16e1ff405808ae77fc5360a423" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:15.761ex; height:5.676ex;" alt="{\displaystyle {\vec {F}}=-{\frac {GMm}{r^{2}}}{\hat {r}},}"></span></dd></dl> <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 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> is the lens-corpuscle separation. If we equate this force with <a href="/wiki/Newton%27s_second_law" class="mw-redirect" title="Newton's second law">Newton's second law</a>, we can solve for the acceleration that the light undergoes: </p> <dl><dd><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 {\vec {a}}=-{\frac {GM}{r^{2}}}{\hat {r}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>G</mi> <mi>M</mi> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {a}}=-{\frac {GM}{r^{2}}}{\hat {r}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ebfac687021bb4f1ee7c7d7ca8858a25e4f4741" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:13.18ex; height:5.676ex;" alt="{\displaystyle {\vec {a}}=-{\frac {GM}{r^{2}}}{\hat {r}}.}"></span></dd></dl> <p>The light interacts with the lens from initial time <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 t=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43469ec032d858feae5aa87029e22eaaf0109e9c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.101ex; height:2.176ex;" alt="{\displaystyle t=0}"></span> 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 t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span>, and the velocity boost the corpuscle receives is </p> <dl><dd><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 \Delta {\vec {v}}=-\int _{0}^{t}dt'\,{\frac {GM}{r(t')^{2}}}{\hat {r}}(t').}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msubsup> <mi>d</mi> <msup> <mi>t</mi> <mo>′</mo> </msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>G</mi> <mi>M</mi> </mrow> <mrow> <mi>r</mi> <mo stretchy="false">(</mo> <msup> <mi>t</mi> <mo>′</mo> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <msup> <mi>t</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta {\vec {v}}=-\int _{0}^{t}dt'\,{\frac {GM}{r(t')^{2}}}{\hat {r}}(t').}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d54cc3d22b66998c01d987f286a8b21beae9ca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:26.754ex; height:6.509ex;" alt="{\displaystyle \Delta {\vec {v}}=-\int _{0}^{t}dt'\,{\frac {GM}{r(t')^{2}}}{\hat {r}}(t').}"></span></dd></dl> <p>If one assumes that initially the light is far enough from the lens to neglect gravity, the perpendicular distance between the light's initial trajectory and the lens is <i>b</i> (the <a href="/wiki/Impact_parameter" title="Impact parameter">impact parameter</a>), and the parallel distance is <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_{\parallel }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∥</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{\parallel }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7eda0ec56fbb038bf6f1c925d68a2d164413c08" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:2.103ex; height:2.509ex;" alt="{\displaystyle r_{\parallel }}"></span>, such that <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^{2}=b^{2}+r_{\parallel }^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msubsup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∥</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r^{2}=b^{2}+r_{\parallel }^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba3717fcabf61ddaea25e7d972b7539afa8a89d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:12.196ex; height:3.843ex;" alt="{\displaystyle r^{2}=b^{2}+r_{\parallel }^{2}}"></span>. We additionally assume a constant speed of light along the parallel direction, <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 dr_{\parallel }\approx c\,dt}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∥</mo> </mrow> </msub> <mo>≈</mo> <mi>c</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dr_{\parallel }\approx c\,dt}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77b2cd9543fcb8b7558757a0347cb7db7659e626" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:9.867ex; height:3.009ex;" alt="{\displaystyle dr_{\parallel }\approx c\,dt}"></span>, and that the light is only being deflected a small amount. After plugging these assumptions into the above equation and further simplifying, one can solve for the velocity boost in the perpendicular direction. The angle of deflection between the corpuscle’s initial and final trajectories is therefore (see, e.g., M. Meneghetti 2021)<sup id="cite_ref-Meneghetti_25-1" class="reference"><a href="#cite_note-Meneghetti-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><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 \theta ={\frac {2GM}{c^{2}r}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>G</mi> <mi>M</mi> </mrow> <mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>r</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta ={\frac {2GM}{c^{2}r}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/195f0223271123e5f41e361e605e43bc776e1727" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:11.103ex; height:5.676ex;" alt="{\displaystyle \theta ={\frac {2GM}{c^{2}r}}.}"></span></dd></dl> <p>Although this result appears to be half the prediction from general relativity, classical physics predicts that the speed of light <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span> is observer-dependent (see, e.g., L. Susskind and A. Friedman 2018)<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> which was superseded by a universal speed of light in <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Explanation_in_terms_of_spacetime_curvature">Explanation in terms of spacetime curvature</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gravitational_lens&action=edit&section=4" title="Edit section: Explanation in terms of spacetime curvature"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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">See also: <a href="/wiki/Kepler_problem_in_general_relativity" class="mw-redirect" title="Kepler problem in general relativity">Kepler problem in general relativity</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Black_hole_lensing_web.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Black_hole_lensing_web.gif/220px-Black_hole_lensing_web.gif" decoding="async" width="220" height="176" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/0/03/Black_hole_lensing_web.gif 1.5x" data-file-width="240" data-file-height="192" /></a><figcaption>Simulated gravitational lensing (black hole passing in front of a background galaxy)</figcaption></figure> <p>In general relativity, light follows the curvature of spacetime, hence when light passes around a massive object, it is bent. This means that the light from an object on the other side will be bent towards an observer's eye, just like an ordinary lens. In general relativity the path of light depends on the shape of space (i.e. the metric). The gravitational attraction can be viewed as the motion of undisturbed objects in a background curved <i><a href="/wiki/Geometry" title="Geometry">geometry</a></i> or alternatively as the response of objects to a <i>force</i> in a flat geometry. The angle of deflection is </p> <dl><dd><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 \theta ={\frac {4GM}{c^{2}r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4</mn> <mi>G</mi> <mi>M</mi> </mrow> <mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>r</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta ={\frac {4GM}{c^{2}r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ae0494fc16b60c7d7f41348ee31d8b615e56ac8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:10.456ex; height:5.676ex;" alt="{\displaystyle \theta ={\frac {4GM}{c^{2}r}}}"></span></dd></dl> <p>toward the mass <i>M</i> at a distance <i>r</i> from the affected radiation, where <i>G</i> is the <a href="/wiki/Gravitational_constant" title="Gravitational constant">universal constant of gravitation</a>, and <i>c</i> is the speed of light in vacuum. </p><p>Since the <a href="/wiki/Schwarzschild_radius" title="Schwarzschild radius">Schwarzschild radius</a> <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_{\text{s}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{\text{s}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5dc67a392f63faf10fdb2eee39b5f382dbb5a936" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.929ex; height:2.009ex;" alt="{\displaystyle r_{\text{s}}}"></span> is defined as <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_{\text{s}}=2Gm/c^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> <mo>=</mo> <mn>2</mn> <mi>G</mi> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{\text{s}}=2Gm/c^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f518b5f9e0fd247890a01e7800c766b96e041b61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.28ex; height:3.176ex;" alt="{\displaystyle r_{\text{s}}=2Gm/c^{2}}"></span>, and <a href="/wiki/Escape_velocity" title="Escape velocity">escape velocity</a> <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 v_{\text{e}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>e</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\text{e}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0ad4222c764f1a57fe3e1f48d1e24419ea8ebfa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.09ex; height:2.009ex;" alt="{\displaystyle v_{\text{e}}}"></span> is defined as <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="{\textstyle v_{\text{e}}={\sqrt {2Gm/r}}=\beta _{\text{e}}c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>e</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> <mi>G</mi> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>r</mi> </msqrt> </mrow> <mo>=</mo> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>e</mtext> </mrow> </msub> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle v_{\text{e}}={\sqrt {2Gm/r}}=\beta _{\text{e}}c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03180f037ec2f6d0c757ff2db0d7308bfc121dd0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:21.136ex; height:3.343ex;" alt="{\textstyle v_{\text{e}}={\sqrt {2Gm/r}}=\beta _{\text{e}}c}"></span>, this can also be expressed in simple form as </p> <dl><dd><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 \theta =2{\frac {r_{\text{s}}}{r}}=2\left({\frac {v_{\text{e}}}{c}}\right)^{2}=2\beta _{\text{e}}^{2}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> <mo>=</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> <mi>r</mi> </mfrac> </mrow> <mo>=</mo> <mn>2</mn> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>e</mtext> </mrow> </msub> <mi>c</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>2</mn> <msubsup> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>e</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta =2{\frac {r_{\text{s}}}{r}}=2\left({\frac {v_{\text{e}}}{c}}\right)^{2}=2\beta _{\text{e}}^{2}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4129c7bf85fa90c07587b7d413df2c523c1cd4c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:26.432ex; height:5.176ex;" alt="{\displaystyle \theta =2{\frac {r_{\text{s}}}{r}}=2\left({\frac {v_{\text{e}}}{c}}\right)^{2}=2\beta _{\text{e}}^{2}.}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Search_for_gravitational_lenses">Search for gravitational lenses</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gravitational_lens&action=edit&section=5" title="Edit section: Search for gravitational lenses"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:MACS_J1206.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/MACS_J1206.jpg/220px-MACS_J1206.jpg" decoding="async" width="220" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/MACS_J1206.jpg/330px-MACS_J1206.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/56/MACS_J1206.jpg/440px-MACS_J1206.jpg 2x" data-file-width="2564" data-file-height="2328" /></a><figcaption>This image from the NASA/ESA Hubble Space Telescope shows the galaxy cluster <a href="/w/index.php?title=MACS_J1206&action=edit&redlink=1" class="new" title="MACS J1206 (page does not exist)">MACS J1206</a>.</figcaption></figure> <p>Most of the gravitational lenses in the past have been discovered accidentally. A search for gravitational lenses in the northern hemisphere (Cosmic Lens All Sky Survey, CLASS), done in radio frequencies using the Very Large Array (VLA) in New Mexico, led to the discovery of 22 new lensing systems, a major milestone. This has opened a whole new avenue for research ranging from finding very distant objects to finding values for cosmological parameters so we can understand the universe better. </p><p>A similar search in the southern hemisphere would be a very good step towards complementing the northern hemisphere search as well as obtaining other objectives for study. If such a search is done using well-calibrated and well-parameterized instruments and data, a result similar to the northern survey can be expected. The use of the Australia Telescope 20 GHz (AT20G) Survey data collected using the Australia Telescope Compact Array (ATCA) stands to be such a collection of data. As the data were collected using the same instrument maintaining a very stringent quality of data we should expect to obtain good results from the search. The AT20G survey is a blind survey at 20 GHz frequency in the radio domain of the electromagnetic spectrum. Due to the high frequency used, the chances of finding gravitational lenses increases as the relative number of compact core objects (e.g. quasars) are higher (Sadler et al. 2006). This is important as the lensing is easier to detect and identify in simple objects compared to objects with complexity in them. This search involves the use of interferometric methods to identify candidates and follow them up at higher resolution to identify them. Full detail of the project is currently under works for publication. </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Helping_Hubble_SDSS_J0915%2B3826.tif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Helping_Hubble_SDSS_J0915%2B3826.tif/lossy-page1-220px-Helping_Hubble_SDSS_J0915%2B3826.tif.jpg" decoding="async" width="220" height="174" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Helping_Hubble_SDSS_J0915%2B3826.tif/lossy-page1-330px-Helping_Hubble_SDSS_J0915%2B3826.tif.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Helping_Hubble_SDSS_J0915%2B3826.tif/lossy-page1-440px-Helping_Hubble_SDSS_J0915%2B3826.tif.jpg 2x" data-file-width="3982" data-file-height="3144" /></a><figcaption>Galaxy cluster SDSS J0915+3826 helps astronomers to study star formation in galaxies.<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></figcaption></figure> <p>Microlensing techniques have been used to search for planets outside our solar system. A statistical analysis of specific cases of observed microlensing over the time period of 2002 to 2007 found that most stars in the <a href="/wiki/Milky_Way" title="Milky Way">Milky Way</a> galaxy hosted at least one orbiting planet within 0.5 to 10 AU.<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>In 2009, weak gravitational lensing was used to extend the mass-X-ray-luminosity relation to older and smaller structures than was previously possible to improve measurements of distant galaxies.<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> </p><p>As of 2013<sup class="plainlinks noexcerpt noprint asof-tag update" style="display:none;"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Gravitational_lens&action=edit">[update]</a></sup> the most distant gravitational lens galaxy, <a href="/wiki/J1000%2B0221" title="J1000+0221">J1000+0221</a>, had been found using <a href="/wiki/NASA" title="NASA">NASA</a>'s <a href="/wiki/Hubble_Space_Telescope" title="Hubble Space Telescope">Hubble Space Telescope</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><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> While it remains the most distant quad-image lensing galaxy known, an even more distant two-image lensing galaxy was subsequently discovered by an international team of astronomers using a combination of <a href="/wiki/Hubble_Space_Telescope" title="Hubble Space Telescope">Hubble Space Telescope</a> and <a href="/wiki/Keck_telescope" class="mw-redirect" title="Keck telescope">Keck telescope</a> imaging and spectroscopy. The discovery and analysis of the <a href="/wiki/IRC_0218_lens" class="mw-redirect" title="IRC 0218 lens">IRC 0218 lens</a> was published in the <i><a href="/wiki/Astrophysical_Journal_Letters" class="mw-redirect" title="Astrophysical Journal Letters">Astrophysical Journal Letters</a></i> on June 23, 2014.<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> </p><p>Research published Sep 30, 2013 in the online edition of <i><a href="/wiki/Physical_Review_Letters" title="Physical Review Letters">Physical Review Letters</a></i>, led by <a href="/wiki/McGill_University" title="McGill University">McGill University</a> in <a href="/wiki/Montreal" title="Montreal">Montreal</a>, <a href="/wiki/Qu%C3%A9bec" class="mw-redirect" title="Québec">Québec</a>, Canada, has discovered the <a href="/wiki/B-modes" class="mw-redirect" title="B-modes">B-modes</a>, that are formed due to gravitational lensing effect, using <a href="/wiki/National_Science_Foundation" title="National Science Foundation">National Science Foundation</a>'s <a href="/wiki/South_Pole_Telescope" title="South Pole Telescope">South Pole Telescope</a> and with help from the Herschel space observatory. This discovery would open the possibilities of testing the theories of how our universe originated.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup><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> </p> <div class="thumb tnone" style="margin-left:auto;margin-right:auto;overflow:hidden;width:auto;max-width:808px"><div class="thumbinner"><div class="noresize" style="overflow:auto"><span typeof="mw:File"><a href="/wiki/File:14-283-Abell2744-DistantGalaxies-20141016.jpg" class="mw-file-description" title="Abell 2744 galaxy cluster - extremely distant galaxies revealed by gravitational lensing (16 October 2014)."><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/14-283-Abell2744-DistantGalaxies-20141016.jpg/800px-14-283-Abell2744-DistantGalaxies-20141016.jpg" decoding="async" width="800" height="891" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/d/d2/14-283-Abell2744-DistantGalaxies-20141016.jpg 1.5x" data-file-width="1077" data-file-height="1200" /></a></span></div><div class="thumbcaption" style="text-align:center"><div class="magnify"><a href="/wiki/File:14-283-Abell2744-DistantGalaxies-20141016.jpg" title="File:14-283-Abell2744-DistantGalaxies-20141016.jpg"> </a></div><a href="/wiki/Abell_2744" title="Abell 2744">Abell 2744</a> <a href="/wiki/Galaxy_cluster" title="Galaxy cluster">galaxy cluster</a> - extremely distant <a href="/wiki/Galaxies" class="mw-redirect" title="Galaxies">galaxies</a> revealed by <a href="/wiki/Gravitational_lensing" class="mw-redirect" title="Gravitational lensing">gravitational lensing</a> (16 October 2014).<sup id="cite_ref-NASA-20140107_35-0" class="reference"><a href="#cite_note-NASA-20140107-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-NASA-20141016_36-0" class="reference"><a href="#cite_note-NASA-20141016-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup></div></div></div> <div class="mw-heading mw-heading2"><h2 id="Solar_gravitational_lens">Solar gravitational lens</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gravitational_lens&action=edit&section=6" title="Edit section: Solar gravitational lens"><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/Solar_gravitational_lens" title="Solar gravitational lens">Solar gravitational lens</a></div> <p>Albert Einstein predicted in 1936 that rays of light from the same direction that skirt the edges of the <a href="/wiki/Sun" title="Sun">Sun</a> would converge to a focal point approximately 542 <a href="/wiki/Astronomical_unit" title="Astronomical unit">AU</a> from the Sun.<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> Thus, a probe positioned at this distance (or greater) from the Sun could use the Sun as a gravitational lens for magnifying distant objects on the opposite side of the Sun.<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> A probe's location could shift around as needed to select different targets relative to the Sun. </p><p>This distance is far beyond the progress and equipment capabilities of space probes such as <i><a href="/wiki/Voyager_1" title="Voyager 1">Voyager 1</a></i>, and beyond the known planets and dwarf planets, though over thousands of years <a href="/wiki/90377_Sedna" class="mw-redirect" title="90377 Sedna">90377 Sedna</a> will move farther away on its highly elliptical orbit. The high gain for potentially detecting signals through this lens, such as microwaves at the 21-cm <a href="/wiki/Hydrogen_line" title="Hydrogen line">hydrogen line</a>, led to the suggestion by <a href="/wiki/Frank_Drake" title="Frank Drake">Frank Drake</a> in the early days of <a href="/wiki/SETI" class="mw-redirect" title="SETI">SETI</a> that a probe could be sent to this distance. A multipurpose probe SETISAIL and later <a href="/wiki/FOCAL_(spacecraft)" title="FOCAL (spacecraft)">FOCAL</a> was proposed to the ESA in 1993, but is expected to be a difficult task.<sup id="cite_ref-Landis_39-0" class="reference"><a href="#cite_note-Landis-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> If a probe does pass 542 AU, magnification capabilities of the lens will continue to act at farther distances, as the rays that come to a focus at larger distances pass further away from the distortions of the Sun's corona.<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> A critique of the concept was given by Landis,<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> who discussed issues including interference of the solar corona, the high magnification of the target, which will make the design of the mission focal plane difficult, and an analysis of the inherent <a href="/wiki/Spherical_aberration" title="Spherical aberration">spherical aberration</a> of the lens. </p><p>In 2020, NASA physicist <a href="/wiki/Slava_Turyshev" title="Slava Turyshev">Slava Turyshev</a> presented his idea of Direct Multipixel Imaging and Spectroscopy of an Exoplanet with a <a href="/wiki/Solar_gravitational_lens" title="Solar gravitational lens">Solar Gravitational Lens</a> Mission. The lens could reconstruct the exoplanet image with ~25 km-scale surface resolution, enough to see surface features and signs of habitability.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Measuring_weak_lensing">Measuring weak lensing</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gravitational_lens&action=edit&section=7" title="Edit section: Measuring weak lensing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Galaxy_cluster_MACS_J2129-0741_and_lensed_galaxy_MACS2129-1.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/76/Galaxy_cluster_MACS_J2129-0741_and_lensed_galaxy_MACS2129-1.jpg/220px-Galaxy_cluster_MACS_J2129-0741_and_lensed_galaxy_MACS2129-1.jpg" decoding="async" width="220" height="176" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/76/Galaxy_cluster_MACS_J2129-0741_and_lensed_galaxy_MACS2129-1.jpg/330px-Galaxy_cluster_MACS_J2129-0741_and_lensed_galaxy_MACS2129-1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/76/Galaxy_cluster_MACS_J2129-0741_and_lensed_galaxy_MACS2129-1.jpg/440px-Galaxy_cluster_MACS_J2129-0741_and_lensed_galaxy_MACS2129-1.jpg 2x" data-file-width="3528" data-file-height="2822" /></a><figcaption>Galaxy cluster MACS J2129-0741 and lensed galaxy MACS2129-1.<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>Kaiser, Squires and Broadhurst (1995),<sup id="cite_ref-KSB-1995_44-0" class="reference"><a href="#cite_note-KSB-1995-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> Luppino & Kaiser (1997)<sup id="cite_ref-LK-1997_45-0" class="reference"><a href="#cite_note-LK-1997-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> and Hoekstra et al. (1998) prescribed a method to invert the effects of the <a href="/wiki/Point_spread_function" title="Point spread function">point spread function</a> (PSF) smearing and shearing, recovering a shear estimator uncontaminated by the systematic distortion of the PSF. This method (KSB+) is the most widely used method in weak lensing shear measurements.<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> </p><p>Galaxies have random rotations and inclinations. As a result, the shear effects in weak lensing need to be determined by statistically preferred orientations. The primary source of error in lensing measurement is due to the convolution of the PSF with the lensed image. The KSB method measures the ellipticity of a galaxy image. The shear is proportional to the ellipticity. The objects in lensed images are parameterized according to their weighted quadrupole moments. For a perfect ellipse, the weighted quadrupole moments are related to the weighted ellipticity. KSB calculate how a weighted ellipticity measure is related to the shear and use the same formalism to remove the effects of the PSF.<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> </p><p>KSB's primary advantages are its mathematical ease and relatively simple implementation. However, KSB is based on a key assumption that the PSF is circular with an anisotropic distortion. This is a reasonable assumption for cosmic shear surveys, but the next generation of surveys (e.g. <a href="/wiki/Large_Synoptic_Survey_Telescope" class="mw-redirect" title="Large Synoptic Survey Telescope">LSST</a>) may need much better accuracy than KSB can provide. </p> <div class="mw-heading mw-heading2"><h2 id="Gallery">Gallery</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gravitational_lens&action=edit&section=8" title="Edit section: Gallery"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:The_Sunburst_Arc_PSZ1_G311.65-18.48.jpg" class="mw-file-description" title="Sunburst Arc galaxy.[49]"><img alt="Sunburst Arc galaxy.[49]" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/The_Sunburst_Arc_PSZ1_G311.65-18.48.jpg/120px-The_Sunburst_Arc_PSZ1_G311.65-18.48.jpg" decoding="async" width="120" height="107" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/The_Sunburst_Arc_PSZ1_G311.65-18.48.jpg/180px-The_Sunburst_Arc_PSZ1_G311.65-18.48.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/08/The_Sunburst_Arc_PSZ1_G311.65-18.48.jpg/240px-The_Sunburst_Arc_PSZ1_G311.65-18.48.jpg 2x" data-file-width="5290" data-file-height="4722" /></a></span></div> <div class="gallerytext">Sunburst Arc galaxy.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Hubble%E2%80%99s_view_on_distant_quasar_J043947.08%2B163415.7.tif" class="mw-file-description" title="Gravitationally lensed Quasar.[50]"><img alt="Gravitationally lensed Quasar.[50]" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Hubble%E2%80%99s_view_on_distant_quasar_J043947.08%2B163415.7.tif/lossy-page1-120px-Hubble%E2%80%99s_view_on_distant_quasar_J043947.08%2B163415.7.tif.jpg" decoding="async" width="120" height="115" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Hubble%E2%80%99s_view_on_distant_quasar_J043947.08%2B163415.7.tif/lossy-page1-180px-Hubble%E2%80%99s_view_on_distant_quasar_J043947.08%2B163415.7.tif.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Hubble%E2%80%99s_view_on_distant_quasar_J043947.08%2B163415.7.tif/lossy-page1-240px-Hubble%E2%80%99s_view_on_distant_quasar_J043947.08%2B163415.7.tif.jpg 2x" data-file-width="914" data-file-height="876" /></a></span></div> <div class="gallerytext">Gravitationally lensed Quasar.<sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:On_the_hunt_for_newborn_stars.tif" class="mw-file-description" title="In SDSS J0952+3434, the lower arc-shaped galaxy has the characteristic shape of a galaxy that has been gravitationally lensed.[51]"><img alt="In SDSS J0952+3434, the lower arc-shaped galaxy has the characteristic shape of a galaxy that has been gravitationally lensed.[51]" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/On_the_hunt_for_newborn_stars.tif/lossy-page1-120px-On_the_hunt_for_newborn_stars.tif.jpg" decoding="async" width="120" height="108" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/On_the_hunt_for_newborn_stars.tif/lossy-page1-180px-On_the_hunt_for_newborn_stars.tif.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/52/On_the_hunt_for_newborn_stars.tif/lossy-page1-240px-On_the_hunt_for_newborn_stars.tif.jpg 2x" data-file-width="3425" data-file-height="3093" /></a></span></div> <div class="gallerytext">In SDSS J0952+3434, the lower arc-shaped galaxy has the characteristic shape of a galaxy that has been gravitationally lensed.<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Warped_and_distorted_SDSS_J1050%2B0017.jpg" class="mw-file-description" title="Warped and distorted around SDSS J1050+0017.[52]"><img alt="Warped and distorted around SDSS J1050+0017.[52]" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Warped_and_distorted_SDSS_J1050%2B0017.jpg/120px-Warped_and_distorted_SDSS_J1050%2B0017.jpg" decoding="async" width="120" height="109" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Warped_and_distorted_SDSS_J1050%2B0017.jpg/180px-Warped_and_distorted_SDSS_J1050%2B0017.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/91/Warped_and_distorted_SDSS_J1050%2B0017.jpg/240px-Warped_and_distorted_SDSS_J1050%2B0017.jpg 2x" data-file-width="3417" data-file-height="3100" /></a></span></div> <div class="gallerytext">Warped and distorted around SDSS J1050+0017.<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Stretched_out_image_of_distant_galaxy.jpg" class="mw-file-description" title="Galaxy SPT0615-JD existed when the Universe was just 500 million years old.[53]"><img alt="Galaxy SPT0615-JD existed when the Universe was just 500 million years old.[53]" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Stretched_out_image_of_distant_galaxy.jpg/120px-Stretched_out_image_of_distant_galaxy.jpg" decoding="async" width="120" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Stretched_out_image_of_distant_galaxy.jpg/180px-Stretched_out_image_of_distant_galaxy.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Stretched_out_image_of_distant_galaxy.jpg/240px-Stretched_out_image_of_distant_galaxy.jpg 2x" data-file-width="3876" data-file-height="2907" /></a></span></div> <div class="gallerytext">Galaxy <a href="/wiki/SPT0615-JD" title="SPT0615-JD">SPT0615-JD</a> existed when the Universe was just 500 million years old.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Cosmic_snake_pregnant_with_stars.tif" class="mw-file-description" title="Gravitational lenses found in the DESI Legacy Survey data[54]"><img alt="Gravitational lenses found in the DESI Legacy Survey data[54]" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/82/Cosmic_snake_pregnant_with_stars.tif/lossy-page1-120px-Cosmic_snake_pregnant_with_stars.tif.jpg" decoding="async" width="120" height="91" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/82/Cosmic_snake_pregnant_with_stars.tif/lossy-page1-180px-Cosmic_snake_pregnant_with_stars.tif.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/82/Cosmic_snake_pregnant_with_stars.tif/lossy-page1-240px-Cosmic_snake_pregnant_with_stars.tif.jpg 2x" data-file-width="1115" data-file-height="848" /></a></span></div> <div class="gallerytext">Gravitational lenses found in the DESI Legacy Survey data<sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Gravitational_lenses_found_in_the_DESI_Legacy_Survey_data.jpg" class="mw-file-description" title="Gravitational lenses found in the DESI Legacy Survey data[55]"><img alt="Gravitational lenses found in the DESI Legacy Survey data[55]" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Gravitational_lenses_found_in_the_DESI_Legacy_Survey_data.jpg/120px-Gravitational_lenses_found_in_the_DESI_Legacy_Survey_data.jpg" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Gravitational_lenses_found_in_the_DESI_Legacy_Survey_data.jpg/180px-Gravitational_lenses_found_in_the_DESI_Legacy_Survey_data.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Gravitational_lenses_found_in_the_DESI_Legacy_Survey_data.jpg/240px-Gravitational_lenses_found_in_the_DESI_Legacy_Survey_data.jpg 2x" data-file-width="3840" data-file-height="3840" /></a></span></div> <div class="gallerytext">Gravitational lenses found in the DESI Legacy Survey data<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Hubble_captures_gallery_of_ultra-bright_galaxies.jpg" class="mw-file-description" title="The lensing phenomenon allows for features as small as about 100 light-years or less.[56]"><img alt="The lensing phenomenon allows for features as small as about 100 light-years or less.[56]" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Hubble_captures_gallery_of_ultra-bright_galaxies.jpg/120px-Hubble_captures_gallery_of_ultra-bright_galaxies.jpg" decoding="async" width="120" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Hubble_captures_gallery_of_ultra-bright_galaxies.jpg/180px-Hubble_captures_gallery_of_ultra-bright_galaxies.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/32/Hubble_captures_gallery_of_ultra-bright_galaxies.jpg/240px-Hubble_captures_gallery_of_ultra-bright_galaxies.jpg 2x" data-file-width="3190" data-file-height="2128" /></a></span></div> <div class="gallerytext">The lensing phenomenon allows for features as small as about 100 light-years or less.<sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Detailed_look_at_a_gravitationally_lensed_supernova.jpg" class="mw-file-description" title="Detailed look at a gravitationally lensed type Ia supernova iPTF16geu.[57]"><img alt="Detailed look at a gravitationally lensed type Ia supernova iPTF16geu.[57]" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ab/Detailed_look_at_a_gravitationally_lensed_supernova.jpg/120px-Detailed_look_at_a_gravitationally_lensed_supernova.jpg" decoding="async" width="120" height="85" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ab/Detailed_look_at_a_gravitationally_lensed_supernova.jpg/180px-Detailed_look_at_a_gravitationally_lensed_supernova.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ab/Detailed_look_at_a_gravitationally_lensed_supernova.jpg/240px-Detailed_look_at_a_gravitationally_lensed_supernova.jpg 2x" data-file-width="1280" data-file-height="905" /></a></span></div> <div class="gallerytext">Detailed look at a gravitationally lensed <a href="/wiki/Type_Ia_supernova" title="Type Ia supernova">type Ia supernova</a> <a href="/w/index.php?title=IPTF16geu&action=edit&redlink=1" class="new" title="IPTF16geu (page does not exist)">iPTF16geu</a>.<sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:HST-Smiling-GalaxyClusterSDSS-J1038%2B4849-20150210.jpg" class="mw-file-description" title=""Smiley" image of galaxy cluster (SDSS J1038+4849) & gravitational lensing (an Einstein ring) (HST).[58]"><img alt=""Smiley" image of galaxy cluster (SDSS J1038+4849) & gravitational lensing (an Einstein ring) (HST).[58]" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/HST-Smiling-GalaxyClusterSDSS-J1038%2B4849-20150210.jpg/120px-HST-Smiling-GalaxyClusterSDSS-J1038%2B4849-20150210.jpg" decoding="async" width="120" height="118" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/HST-Smiling-GalaxyClusterSDSS-J1038%2B4849-20150210.jpg/180px-HST-Smiling-GalaxyClusterSDSS-J1038%2B4849-20150210.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b9/HST-Smiling-GalaxyClusterSDSS-J1038%2B4849-20150210.jpg/240px-HST-Smiling-GalaxyClusterSDSS-J1038%2B4849-20150210.jpg 2x" data-file-width="1280" data-file-height="1263" /></a></span></div> <div class="gallerytext">"Smiley" image of <a href="/wiki/Galaxy_cluster" title="Galaxy cluster">galaxy cluster</a> (SDSS J1038+4849) & gravitational lensing (an <a href="/wiki/Einstein_ring" title="Einstein ring">Einstein ring</a>) (<a href="/wiki/Hubble_Space_Telescope" title="Hubble Space Telescope">HST</a>).<sup id="cite_ref-NASA-20150210_58-0" class="reference"><a href="#cite_note-NASA-20150210-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Gravitationell-lins-4.jpg" class="mw-file-description" title="Abell 1689 - actual gravitational lensing effects (Hubble Space Telescope)."><img alt="Abell 1689 - actual gravitational lensing effects (Hubble Space Telescope)." src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Gravitationell-lins-4.jpg/116px-Gravitationell-lins-4.jpg" decoding="async" width="116" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Gravitationell-lins-4.jpg/173px-Gravitationell-lins-4.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Gravitationell-lins-4.jpg/231px-Gravitationell-lins-4.jpg 2x" data-file-width="3853" data-file-height="4000" /></a></span></div> <div class="gallerytext"><a href="/wiki/Abell_1689" title="Abell 1689">Abell 1689</a> - actual gravitational lensing effects (<a href="/wiki/Hubble_Space_Telescope" title="Hubble Space Telescope">Hubble Space Telescope</a>).</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:COSMOS_3D_dark_matter_map.jpg" class="mw-file-description" title="Dark matter distribution - weak gravitational lensing (Hubble Space Telescope)."><img alt="Dark matter distribution - weak gravitational lensing (Hubble Space Telescope)." src="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/COSMOS_3D_dark_matter_map.jpg/120px-COSMOS_3D_dark_matter_map.jpg" decoding="async" width="120" height="91" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/COSMOS_3D_dark_matter_map.jpg/180px-COSMOS_3D_dark_matter_map.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/38/COSMOS_3D_dark_matter_map.jpg/240px-COSMOS_3D_dark_matter_map.jpg 2x" data-file-width="2823" data-file-height="2146" /></a></span></div> <div class="gallerytext"><a href="/wiki/Dark_matter" title="Dark matter">Dark matter</a> distribution - weak gravitational lensing (<a href="/wiki/Hubble_Space_Telescope" title="Hubble Space Telescope">Hubble Space Telescope</a>).</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:The_most_distant_gravitational_lens_yet_discovered.jpg" class="mw-file-description" title="Gravitational lens discovered at redshift z = 1.53.[59]"><img alt="Gravitational lens discovered at redshift z = 1.53.[59]" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/The_most_distant_gravitational_lens_yet_discovered.jpg/120px-The_most_distant_gravitational_lens_yet_discovered.jpg" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/The_most_distant_gravitational_lens_yet_discovered.jpg/180px-The_most_distant_gravitational_lens_yet_discovered.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/83/The_most_distant_gravitational_lens_yet_discovered.jpg/240px-The_most_distant_gravitational_lens_yet_discovered.jpg 2x" data-file-width="505" data-file-height="505" /></a></span></div> <div class="gallerytext">Gravitational lens discovered at <a href="/wiki/Redshift" title="Redshift">redshift</a> z = 1.53.<sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:PIA23641-GravitationalLensing-20200108.jpg" class="mw-file-description" title="Gravitational Lensing Graphic (January 8, 2020)"><img alt="Gravitational Lensing Graphic (January 8, 2020)" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a8/PIA23641-GravitationalLensing-20200108.jpg/120px-PIA23641-GravitationalLensing-20200108.jpg" decoding="async" width="120" height="63" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a8/PIA23641-GravitationalLensing-20200108.jpg/180px-PIA23641-GravitationalLensing-20200108.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a8/PIA23641-GravitationalLensing-20200108.jpg/240px-PIA23641-GravitationalLensing-20200108.jpg 2x" data-file-width="4096" data-file-height="2160" /></a></span></div> <div class="gallerytext">Gravitational Lensing Graphic (January 8, 2020)</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Hubble_Showcases_Hamilton%E2%80%99s_Object.jpg" class="mw-file-description" title="Hubble Showcases Hamilton's Object"><img alt="Hubble Showcases Hamilton's Object" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Hubble_Showcases_Hamilton%E2%80%99s_Object.jpg/120px-Hubble_Showcases_Hamilton%E2%80%99s_Object.jpg" decoding="async" width="120" height="96" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Hubble_Showcases_Hamilton%E2%80%99s_Object.jpg/180px-Hubble_Showcases_Hamilton%E2%80%99s_Object.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/24/Hubble_Showcases_Hamilton%E2%80%99s_Object.jpg/240px-Hubble_Showcases_Hamilton%E2%80%99s_Object.jpg 2x" data-file-width="1280" data-file-height="1024" /></a></span></div> <div class="gallerytext">Hubble Showcases Hamilton's Object</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Gravitational_lensing_by_a_black_hole.jpg" class="mw-file-description" title="Illustration of gravitational lensing[60]"><img alt="Illustration of gravitational lensing[60]" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Gravitational_lensing_by_a_black_hole.jpg/120px-Gravitational_lensing_by_a_black_hole.jpg" decoding="async" width="120" height="68" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Gravitational_lensing_by_a_black_hole.jpg/180px-Gravitational_lensing_by_a_black_hole.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Gravitational_lensing_by_a_black_hole.jpg/240px-Gravitational_lensing_by_a_black_hole.jpg 2x" data-file-width="1280" data-file-height="720" /></a></span></div> <div class="gallerytext">Illustration of gravitational lensing<sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Gravitationally-lensed_distant_star-forming_galaxy.jpg" class="mw-file-description" title="Gravitationally-lensed distant star-forming galaxies.[61]"><img alt="Gravitationally-lensed distant star-forming galaxies.[61]" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Gravitationally-lensed_distant_star-forming_galaxy.jpg/120px-Gravitationally-lensed_distant_star-forming_galaxy.jpg" decoding="async" width="120" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Gravitationally-lensed_distant_star-forming_galaxy.jpg/180px-Gravitationally-lensed_distant_star-forming_galaxy.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Gravitationally-lensed_distant_star-forming_galaxy.jpg/240px-Gravitationally-lensed_distant_star-forming_galaxy.jpg 2x" data-file-width="2559" data-file-height="525" /></a></span></div> <div class="gallerytext">Gravitationally-lensed distant star-forming galaxies.<sup id="cite_ref-61" class="reference"><a href="#cite_note-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup></div> </li> </ul> <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=Gravitational_lens&action=edit&section=9" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Terrestrial_atmospheric_lens" title="Terrestrial atmospheric lens">Terrestrial atmospheric lens</a></li> <li><a href="/wiki/Galactic_lens" title="Galactic lens">Galactic lens</a> – Structure of galaxies</li> <li><a href="/wiki/Gravitational_lensing_formalism" title="Gravitational lensing formalism">Gravitational lensing formalism</a> – type of formalism<span style="display:none" class="category-wikidata-fallback-annotation">Pages displaying wikidata descriptions as a fallback</span></li> <li><a href="/wiki/Strong_gravitational_lensing" title="Strong gravitational lensing">Strong gravitational lensing</a> – effect strong enough to produce multiple images, arcs, or even Einstein rings<span style="display:none" class="category-wikidata-fallback-annotation">Pages displaying wikidata descriptions as a fallback</span> <ul><li><a href="/wiki/Einstein_cross" class="mw-redirect" title="Einstein cross">Einstein cross</a> – Gravitationally lensed image of a quasar<span style="display:none" class="category-annotation-with-redirected-description">Pages displaying short descriptions of redirect targets</span></li> <li><a href="/wiki/Einstein_ring" title="Einstein ring">Einstein ring</a> – Feature seen when light is gravitationally lensed by an object</li></ul></li> <li><a href="/wiki/Weak_gravitational_lensing" title="Weak gravitational lensing">Weak gravitational lensing</a> – gravitational deflection of light without creating noticeable extra images<span style="display:none" class="category-wikidata-fallback-annotation">Pages displaying wikidata descriptions as a fallback</span></li> <li><a href="/wiki/Gravitational_microlensing" title="Gravitational microlensing">Gravitational microlensing</a> – Astronomical phenomenon due to the gravitational lens effect</li> <li><a href="/wiki/SN_Refsdal" title="SN Refsdal">SN Refsdal</a> – Supernova that has been lensed</li> <li><a href="/wiki/Euclid_(spacecraft)" title="Euclid (spacecraft)">Euclid (spacecraft)</a> – European visible and near-infrared space observatory</li></ul> <div class="mw-heading mw-heading2"><h2 id="Historical_papers_and_references">Historical papers and references</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gravitational_lens&action=edit&section=10" title="Edit section: Historical papers and references"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><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="CITEREFChwolson1924" class="citation journal cs1 cs1-prop-foreign-lang-source">Chwolson, O. (1924). "Über eine mögliche Form fiktiver Doppelsterne". <i>Astronomische Nachrichten</i> (in German). <b>221</b> (20): 329–330. <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/1924AN....221..329C">1924AN....221..329C</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%2Fasna.19242212003">10.1002/asna.19242212003</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Astronomische+Nachrichten&rft.atitle=%C3%9Cber+eine+m%C3%B6gliche+Form+fiktiver+Doppelsterne&rft.volume=221&rft.issue=20&rft.pages=329-330&rft.date=1924&rft_id=info%3Adoi%2F10.1002%2Fasna.19242212003&rft_id=info%3Abibcode%2F1924AN....221..329C&rft.aulast=Chwolson&rft.aufirst=O.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEinstein1936" class="citation journal cs1"><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein, Albert</a> (1936). "Lens-like Action of a Star by the Deviation of Light in the Gravitational Field". <i>Science</i>. <b>84</b> (2188): 506–507. <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/1936Sci....84..506E">1936Sci....84..506E</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.84.2188.506">10.1126/science.84.2188.506</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/1663250">1663250</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/17769014">17769014</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:38450435">38450435</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Science&rft.atitle=Lens-like+Action+of+a+Star+by+the+Deviation+of+Light+in+the+Gravitational+Field&rft.volume=84&rft.issue=2188&rft.pages=506-507&rft.date=1936&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A38450435%23id-name%3DS2CID&rft_id=info%3Abibcode%2F1936Sci....84..506E&rft_id=info%3Apmid%2F17769014&rft_id=info%3Adoi%2F10.1126%2Fscience.84.2188.506&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1663250%23id-name%3DJSTOR&rft.aulast=Einstein&rft.aufirst=Albert&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRennTilman_SauerJohn_Stachel1997" class="citation journal cs1"><a href="/wiki/J%C3%BCrgen_Renn" title="Jürgen Renn">Renn, Jürgen</a>; <a href="/wiki/Tilman_Sauer" title="Tilman Sauer">Tilman Sauer</a>; <a href="/wiki/John_Stachel" title="John Stachel">John Stachel</a> (1997). "The Origin of Gravitational Lensing: A Postscript to Einstein's 1936 Science paper". <i>Science</i>. <b>275</b> (5297): 184–186. <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/1997Sci...275..184R">1997Sci...275..184R</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.275.5297.184">10.1126/science.275.5297.184</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/8985006">8985006</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:43449111">43449111</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Science&rft.atitle=The+Origin+of+Gravitational+Lensing%3A+A+Postscript+to+Einstein%27s+1936+Science+paper&rft.volume=275&rft.issue=5297&rft.pages=184-186&rft.date=1997&rft_id=info%3Adoi%2F10.1126%2Fscience.275.5297.184&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A43449111%23id-name%3DS2CID&rft_id=info%3Apmid%2F8985006&rft_id=info%3Abibcode%2F1997Sci...275..184R&rft.aulast=Renn&rft.aufirst=J%C3%BCrgen&rft.au=Tilman+Sauer&rft.au=John+Stachel&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" class="Z3988"></span></li></ul> <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=Gravitational_lens&action=edit&section=11" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dt>Notes</dt></dl> <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 reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-NYT-20150305-video-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-NYT-20150305-video_1-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDrakefordCorumOverbye2015" class="citation news cs1">Drakeford, Jason; Corum, Jonathan; Overbye, Dennis (March 5, 2015). <a rel="nofollow" class="external text" href="https://www.nytimes.com/video/science/100000003552687/out-there-einsteins-telescope.html">"Einstein's Telescope - video (02:32)"</a>. <i><a href="/wiki/New_York_Times" class="mw-redirect" title="New York Times">New York Times</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">December 27,</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=New+York+Times&rft.atitle=Einstein%27s+Telescope+-+video+%2802%3A32%29&rft.date=2015-03-05&rft.aulast=Drakeford&rft.aufirst=Jason&rft.au=Corum%2C+Jonathan&rft.au=Overbye%2C+Dennis&rft_id=https%3A%2F%2Fwww.nytimes.com%2Fvideo%2Fscience%2F100000003552687%2Fout-there-einsteins-telescope.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" class="Z3988"></span></span> </li> <li id="cite_note-NYT-20150305-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-NYT-20150305_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOverbye2015" class="citation news cs1"><a href="/wiki/Dennis_Overbye" title="Dennis Overbye">Overbye, Dennis</a> (March 5, 2015). <a rel="nofollow" class="external text" href="https://www.nytimes.com/2015/03/06/science/astronomers-observe-supernova-and-find-theyre-watching-reruns.html">"Astronomers Observe Supernova and Find They're Watching Reruns"</a>. <i><a href="/wiki/New_York_Times" class="mw-redirect" title="New York Times">New York Times</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">March 5,</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=New+York+Times&rft.atitle=Astronomers+Observe+Supernova+and+Find+They%27re+Watching+Reruns&rft.date=2015-03-05&rft.aulast=Overbye&rft.aufirst=Dennis&rft_id=https%3A%2F%2Fwww.nytimes.com%2F2015%2F03%2F06%2Fscience%2Fastronomers-observe-supernova-and-find-theyre-watching-reruns.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" 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="CITEREFBernard_F._Schutz1985" class="citation book cs1">Bernard F. Schutz (1985). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=qhDFuWbLlgQC"><i>A First Course in General Relativity</i></a> (illustrated, herdruk ed.). Cambridge University Press. p. 295. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-27703-7" title="Special:BookSources/978-0-521-27703-7"><bdi>978-0-521-27703-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+First+Course+in+General+Relativity&rft.pages=295&rft.edition=illustrated%2C+herdruk&rft.pub=Cambridge+University+Press&rft.date=1985&rft.isbn=978-0-521-27703-7&rft.au=Bernard+F.+Schutz&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DqhDFuWbLlgQC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" 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="CITEREFWolfgang_Rindler2006" class="citation book cs1">Wolfgang Rindler (2006). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=UQpREAAAQBAJ"><i>Relativity: Special, General, and Cosmological</i></a> (2nd ed.). OUP Oxford. p. 21. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-152433-2" title="Special:BookSources/978-0-19-152433-2"><bdi>978-0-19-152433-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Relativity%3A+Special%2C+General%2C+and+Cosmological&rft.pages=21&rft.edition=2nd&rft.pub=OUP+Oxford&rft.date=2006&rft.isbn=978-0-19-152433-2&rft.au=Wolfgang+Rindler&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DUQpREAAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" class="Z3988"></span> <a rel="nofollow" class="external text" href="https://books.google.com/books?id=UQpREAAAQBAJ&pg=PA21">Extract of page 21</a></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 id="CITEREFGabor_KunstatterJeffrey_G_WilliamsD_E_Vincent1992" class="citation book cs1">Gabor Kunstatter; Jeffrey G Williams; D E Vincent (1992). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ukJBDwAAQBAJ"><i>General Relativity And Relativistic Astrophysics - Proceedings Of The 4th Canadian Conference</i></a>. World Scientific. p. 100. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-981-4554-87-9" title="Special:BookSources/978-981-4554-87-9"><bdi>978-981-4554-87-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=General+Relativity+And+Relativistic+Astrophysics+-+Proceedings+Of+The+4th+Canadian+Conference&rft.pages=100&rft.pub=World+Scientific&rft.date=1992&rft.isbn=978-981-4554-87-9&rft.au=Gabor+Kunstatter&rft.au=Jeffrey+G+Williams&rft.au=D+E+Vincent&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DukJBDwAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" class="Z3988"></span> <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ukJBDwAAQBAJ&pg=PA100">Extract of page 100</a></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="CITEREFPekka_TeerikorpiMauri_ValtonenK._LehtoHarry_Lehto2008" class="citation book cs1">Pekka Teerikorpi; Mauri Valtonen; K. Lehto; Harry Lehto; Gene Byrd; Arthur Chernin (2008). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=sNmtKZnUg-sC"><i>The Evolving Universe and the Origin of Life: The Search for Our Cosmic Roots</i></a> (illustrated ed.). Springer Science & Business Media. p. 165. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-09534-9" title="Special:BookSources/978-0-387-09534-9"><bdi>978-0-387-09534-9</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+Evolving+Universe+and+the+Origin+of+Life%3A+The+Search+for+Our+Cosmic+Roots&rft.pages=165&rft.edition=illustrated&rft.pub=Springer+Science+%26+Business+Media&rft.date=2008&rft.isbn=978-0-387-09534-9&rft.au=Pekka+Teerikorpi&rft.au=Mauri+Valtonen&rft.au=K.+Lehto&rft.au=Harry+Lehto&rft.au=Gene+Byrd&rft.au=Arthur+Chernin&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DsNmtKZnUg-sC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" class="Z3988"></span> <a rel="nofollow" class="external text" href="https://books.google.com/books?id=sNmtKZnUg-sC&pg=PA165">Extract of page 165</a></span> </li> <li id="cite_note-Early_History_of_Gravitational_Lensing-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-Early_History_of_Gravitational_Lensing_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Early_History_of_Gravitational_Lensing_7-1"><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="CITEREFTurner2006" class="citation web cs1">Turner, Christina (February 14, 2006). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080725085534/http://www.nd.edu/%7Ehps/turner.pdf">"The Early History of Gravitational Lensing"</a> <span class="cs1-format">(PDF)</span>. Archived from <a rel="nofollow" class="external text" href="http://www.nd.edu/~hps/turner.pdf">the original</a> <span class="cs1-format">(PDF)</span> on July 25, 2008.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Early+History+of+Gravitational+Lensing&rft.date=2006-02-14&rft.aulast=Turner&rft.aufirst=Christina&rft_id=http%3A%2F%2Fwww.nd.edu%2F~hps%2Fturner.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" 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="CITEREFBičákLedvinka2014" class="citation book cs1">Bičák, Jiří; Ledvinka, Tomáš (2014). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Ax0qBAAAQBAJ&pg=PA49"><i>General Relativity, Cosmology and Astrophysics: Perspectives 100 years after Einstein's stay in Prague</i></a> (illustrated ed.). Springer. pp. 49–50. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9783319063492" title="Special:BookSources/9783319063492"><bdi>9783319063492</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=General+Relativity%2C+Cosmology+and+Astrophysics%3A+Perspectives+100+years+after+Einstein%27s+stay+in+Prague&rft.pages=49-50&rft.edition=illustrated&rft.pub=Springer&rft.date=2014&rft.isbn=9783319063492&rft.aulast=Bi%C4%8D%C3%A1k&rft.aufirst=Ji%C5%99%C3%AD&rft.au=Ledvinka%2C+Tom%C3%A1%C5%A1&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DAx0qBAAAQBAJ%26pg%3DPA49&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" class="Z3988"></span></span> </li> <li id="cite_note-origin_of_the_idea-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-origin_of_the_idea_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-origin_of_the_idea_9-1"><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="CITEREFTilman_Sauer2008" class="citation journal cs1">Tilman Sauer (2008). "Nova Geminorum 1912 and the Origin of the Idea of Gravitational Lensing". <i>Archive for History of Exact Sciences</i>. <b>62</b> (1): 1–22. <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/0704.0963">0704.0963</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/2008AHES...62....1S">2008AHES...62....1S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs00407-007-0008-4">10.1007/s00407-007-0008-4</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:17384823">17384823</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Archive+for+History+of+Exact+Sciences&rft.atitle=Nova+Geminorum+1912+and+the+Origin+of+the+Idea+of+Gravitational+Lensing&rft.volume=62&rft.issue=1&rft.pages=1-22&rft.date=2008&rft_id=info%3Aarxiv%2F0704.0963&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A17384823%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2Fs00407-007-0008-4&rft_id=info%3Abibcode%2F2008AHES...62....1S&rft.au=Tilman+Sauer&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" class="Z3988"></span></span> </li> <li id="cite_note-:0-10"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_10-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_10-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:0_10-2"><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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20160701154224/http://www.einstein-online.info/spotlights/grav_lensing_history">"A brief history of gravitational lensing"</a>. <i><a href="/wiki/Einstein_Online" class="mw-redirect" title="Einstein Online">Einstein Online</a></i>. <a href="/wiki/Max_Planck_Institute_for_Gravitational_Physics" title="Max Planck Institute for Gravitational Physics">Max Planck Institute for Gravitational Physics</a>. Archived from <a rel="nofollow" class="external text" href="http://www.einstein-online.info/spotlights/grav_lensing_history">the original</a> on 2016-07-01<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-06-29</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Einstein+Online&rft.atitle=A+brief+history+of+gravitational+lensing&rft_id=http%3A%2F%2Fwww.einstein-online.info%2Fspotlights%2Fgrav_lensing_history&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" 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="CITEREFLodge1919" class="citation journal cs1">Lodge, Oliver J. (December 1919). <a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F104354a0">"Gravitation and Light"</a>. <i>Nature</i>. <b>104</b> (2614): 354. <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/1919Natur.104..354L">1919Natur.104..354L</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/10.1038%2F104354a0">10.1038/104354a0</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/0028-0836">0028-0836</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:4157815">4157815</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Gravitation+and+Light&rft.volume=104&rft.issue=2614&rft.pages=354&rft.date=1919-12&rft_id=info%3Adoi%2F10.1038%2F104354a0&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4157815%23id-name%3DS2CID&rft.issn=0028-0836&rft_id=info%3Abibcode%2F1919Natur.104..354L&rft.aulast=Lodge&rft.aufirst=Oliver+J.&rft_id=https%3A%2F%2Fdoi.org%2F10.1038%252F104354a0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.abc.net.au/science/k2/moments/gmis9737.htm">"Gravity Lens – Part 2 (Great Moments in Science, ABS Science)"</a>. <i><a href="/wiki/Australian_Broadcasting_Corporation" title="Australian Broadcasting Corporation">Australian Broadcasting Corporation</a></i>. 5 November 2001.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Australian+Broadcasting+Corporation&rft.atitle=Gravity+Lens+%E2%80%93+Part+2+%28Great+Moments+in+Science%2C+ABS+Science%29&rft.date=2001-11-05&rft_id=http%3A%2F%2Fwww.abc.net.au%2Fscience%2Fk2%2Fmoments%2Fgmis9737.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" class="Z3988"></span></span> </li> <li id="cite_note-Schneider,_Peter;_Ehlers,_Jürgen;_Falco,_Emilio_E._1992-13"><span class="mw-cite-backlink">^ <a href="#cite_ref-Schneider,_Peter;_Ehlers,_Jürgen;_Falco,_Emilio_E._1992_13-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Schneider,_Peter;_Ehlers,_Jürgen;_Falco,_Emilio_E._1992_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="CITEREFSchneider,_PeterEhlers,_JürgenFalco,_Emilio_E.1992" class="citation book cs1">Schneider, Peter; Ehlers, Jürgen; Falco, Emilio E. (1992). <i>Gravitational Lenses</i>. Springer-Verlag Berlin Heidelberg New York Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-97070-5" title="Special:BookSources/978-3-540-97070-5"><bdi>978-3-540-97070-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Gravitational+Lenses&rft.pub=Springer-Verlag+Berlin+Heidelberg+New+York+Press&rft.date=1992&rft.isbn=978-3-540-97070-5&rft.au=Schneider%2C+Peter&rft.au=Ehlers%2C+J%C3%BCrgen&rft.au=Falco%2C+Emilio+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMelia,_Fulvio2007" class="citation book cs1"><a href="/wiki/Fulvio_Melia" title="Fulvio Melia">Melia, Fulvio</a> (2007). <i>The Galactic Supermassive Black Hole</i>. Princeton University Press. pp. 255–256. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-13129-0" title="Special:BookSources/978-0-691-13129-0"><bdi>978-0-691-13129-0</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+Galactic+Supermassive+Black+Hole&rft.pages=255-256&rft.pub=Princeton+University+Press&rft.date=2007&rft.isbn=978-0-691-13129-0&rft.au=Melia%2C+Fulvio&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" 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 id="CITEREFSoldner,_J._G._V.1804" class="citation journal cs1">Soldner, J. G. V. (1804). <span class="cs1-ws-icon" title="s:Translation:On the Deflection of a Light Ray from its Rectilinear Motion"><a class="external text" href="https://en.wikisource.org/wiki/Translation:On_the_Deflection_of_a_Light_Ray_from_its_Rectilinear_Motion">"On the deflection of a light ray from its rectilinear motion, by the attraction of a celestial body at which it nearly passes by" </a></span>. <i>Berliner Astronomisches Jahrbuch</i>: 161–172.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Berliner+Astronomisches+Jahrbuch&rft.atitle=On+the+deflection+of+a+light+ray+from+its+rectilinear+motion%2C+by+the+attraction+of+a+celestial+body+at+which+it+nearly+passes+by&rft.pages=161-172&rft.date=1804&rft.au=Soldner%2C+J.+G.+V.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" class="Z3988"></span></span> </li> <li id="cite_note-Opticks-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-Opticks_16-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1998" class="citation book cs1"><a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton, Isaac</a> (1998). <i>Opticks: or, a treatise of the reflexions, refractions, inflexions and colours of light. Also two treatises of the species and magnitude of curvilinear figures</i>. Commentary by Nicholas Humez (Octavo ed.). Palo Alto, Calif.: Octavo. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-891788-04-8" title="Special:BookSources/978-1-891788-04-8"><bdi>978-1-891788-04-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Opticks%3A+or%2C+a+treatise+of+the+reflexions%2C+refractions%2C+inflexions+and+colours+of+light.+Also+two+treatises+of+the+species+and+magnitude+of+curvilinear+figures.&rft.place=Palo+Alto%2C+Calif.&rft.edition=Octavo&rft.pub=Octavo&rft.date=1998&rft.isbn=978-1-891788-04-8&rft.aulast=Newton&rft.aufirst=Isaac&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" class="Z3988"></span> (<i>Opticks</i> was originally published in 1704).</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="CITEREFWill,_C.M.2006" class="citation journal cs1">Will, C.M. 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Retrieved <span class="nowrap">16 January</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.spacetelescope.org&rft.atitle=Stretched+out+image+of+distant+galaxy&rft_id=https%3A%2F%2Fwww.spacetelescope.org%2Fimages%2Fopo1802a%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.spacetelescope.org/images/potw1747a/">"Cosmic snake pregnant with stars"</a>. <i>www.spacetelescope.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">20 November</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.spacetelescope.org&rft.atitle=Cosmic+snake+pregnant+with+stars&rft_id=http%3A%2F%2Fwww.spacetelescope.org%2Fimages%2Fpotw1747a%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" class="Z3988"></span></span> </li> <li id="cite_note-55"><span class="mw-cite-backlink"><b><a href="#cite_ref-55">^</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://noirlab.edu/public/news/noirlab2104/">"Doubling the Number of Known Gravitational Lenses"</a>. <i>noirlab.edu</i><span class="reference-accessdate">. Retrieved <span class="nowrap">3 February</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=noirlab.edu&rft.atitle=Doubling+the+Number+of+Known+Gravitational+Lenses&rft_id=https%3A%2F%2Fnoirlab.edu%2Fpublic%2Fnews%2Fnoirlab2104%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" class="Z3988"></span></span> </li> <li id="cite_note-56"><span class="mw-cite-backlink"><b><a href="#cite_ref-56">^</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.spacetelescope.org/images/opo1724a/">"Hubble captures gallery of ultra-bright galaxies"</a>. <i>www.spacetelescope.org</i><span class="reference-accessdate">. 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Retrieved <span class="nowrap">21 April</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.spacetelescope.org&rft.atitle=Detailed+look+at+a+gravitationally+lensed+supernova&rft_id=https%3A%2F%2Fwww.spacetelescope.org%2Fimages%2Fheic1710a%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" class="Z3988"></span></span> </li> <li id="cite_note-NASA-20150210-58"><span class="mw-cite-backlink"><b><a href="#cite_ref-NASA-20150210_58-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLoffDunbar2015" class="citation web cs1">Loff, Sarah; Dunbar, Brian (February 10, 2015). <a rel="nofollow" class="external text" href="https://www.nasa.gov/content/hubble-sees-a-smiling-lens/">"Hubble Sees A Smiling Lens"</a>. <i><a href="/wiki/NASA" title="NASA">NASA</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">February 10,</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=NASA&rft.atitle=Hubble+Sees+A+Smiling+Lens&rft.date=2015-02-10&rft.aulast=Loff&rft.aufirst=Sarah&rft.au=Dunbar%2C+Brian&rft_id=http%3A%2F%2Fwww.nasa.gov%2Fcontent%2Fhubble-sees-a-smiling-lens%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" class="Z3988"></span></span> </li> <li id="cite_note-59"><span class="mw-cite-backlink"><b><a href="#cite_ref-59">^</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="http://www.spacetelescope.org/news/heic1319/">"Most distant gravitational lens helps weigh galaxies"</a>. <i>ESA/Hubble Press Release</i><span class="reference-accessdate">. Retrieved <span class="nowrap">18 October</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=ESA%2FHubble+Press+Release&rft.atitle=Most+distant+gravitational+lens+helps+weigh+galaxies&rft_id=http%3A%2F%2Fwww.spacetelescope.org%2Fnews%2Fheic1319%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://hubblesite.org/contents/news-releases/2022/news-2022-001?news=true">"Hubble Determines Mass of Isolated Black Hole Roaming Our Milky Way Galaxy"</a>. <i>HubbleSite.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">16 June</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=HubbleSite.org&rft.atitle=Hubble+Determines+Mass+of+Isolated+Black+Hole+Roaming+Our+Milky+Way+Galaxy&rft_id=https%3A%2F%2Fhubblesite.org%2Fcontents%2Fnews-releases%2F2022%2Fnews-2022-001%3Fnews%3Dtrue&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" 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 class="citation news cs1"><a rel="nofollow" class="external text" href="http://www.eso.org/public/news/eso1313/">"ALMA Rewrites History of Universe's Stellar Baby Boom"</a>. <i>ESO</i>. 13 March 2013<span class="reference-accessdate">. Retrieved <span class="nowrap">2 April</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=ESO&rft.atitle=ALMA+Rewrites+History+of+Universe%27s+Stellar+Baby+Boom&rft.date=2013-03-13&rft_id=http%3A%2F%2Fwww.eso.org%2Fpublic%2Fnews%2Feso1313%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" class="Z3988"></span></span> </li> </ol></div> <dl><dt>Bibliography</dt></dl> <ul><li>"<i><a rel="nofollow" class="external text" href="http://www.sciencenews.org/view/generic/id/33082/title/Math_Trek__Accidental_astrophysicists">Accidental Astrophysicists</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120216201236/http://www.sciencenews.org/view/generic/id/33082/title/Math_Trek__Accidental_astrophysicists">Archived</a> 2012-02-16 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></i>". Science News, June 13, 2008.</li> <li>"<i><a rel="nofollow" class="external text" href="https://web.archive.org/web/20101210135526/http://www.cinespa.ucr.ac.cr/software/xfgl/index.html">XFGLenses</a></i>". A Computer Program to visualize Gravitational Lenses, Francisco Frutos-Alfaro</li> <li>"<i><a rel="nofollow" class="external text" href="https://web.archive.org/web/20070929124804/http://www.btinternet.com/~Boughen/G-LenS">G-LenS</a></i>". A Point Mass Gravitational Lens Simulation, Mark Boughen.</li> <li>Newbury, Pete, "<i><a rel="nofollow" class="external text" href="https://web.archive.org/web/20110523100723/http://www.iam.ubc.ca/old_pages/newbury/lenses/lenses.html">Gravitational Lensing</a></i>". Institute of Applied Mathematics, The University of British Columbia.</li> <li>Cohen, N., "Gravity's Lens: Views of the New Cosmology", Wiley and Sons, 1988.</li> <li>"<i><a rel="nofollow" class="external text" href="http://cfa-www.harvard.edu/~rschild/qgl.html">Q0957+561 Gravitational Lens</a></i>". Harvard.edu.</li> <li>Bridges, Andrew, "<i><a rel="nofollow" class="external text" href="http://www.signonsandiego.com/news/science/20040215-1033-ca-farthestgalaxy.html">Most distant known object in universe discovered</a></i>". <a href="/wiki/Associated_Press" title="Associated Press">Associated Press</a>. February 15, 2004. (Farthest galaxy found by gravitational lensing, using Abell 2218 and Hubble Space Telescope.)</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20070310222247/http://sciencecareers.sciencemag.org/career_development/previous_issues/articles/2006_05_12/analysing_corporations_and_the_cosmos/(parent)/12100">Analyzing Corporations ... and the Cosmos</a> An unusual career path in gravitational lensing.</li> <li>"<i><a rel="nofollow" class="external text" href="http://cfa-www.harvard.edu/castles">HST images of strong gravitational lenses</a></i>". Harvard-Smithsonian Center for Astrophysics.</li> <li>"<i><a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0404309">A planetary microlensing event</a></i>" and "<i><a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0505451">A Jovian-mass Planet in Microlensing Event OGLE-2005-BLG-071</a></i>", the first <a href="/wiki/Extrasolar_planet" class="mw-redirect" title="Extrasolar planet">extra-solar planet</a> detections using microlensing.</li> <li><a rel="nofollow" class="external text" href="http://xstructure.inr.ac.ru/x-bin/theme3.py?level=2&index1=-188353">Gravitational lensing on arxiv.org</a></li> <li><a rel="nofollow" class="external text" href="http://www.aoc.nrao.edu/~smyers/class.html">NRAO CLASS home page</a></li> <li><a rel="nofollow" class="external text" href="http://www.atnf.csiro.au/research/AT20G">AT20G survey</a></li> <li><a rel="nofollow" class="external text" href="http://cdsads.u-strasbg.fr/full/1981Ap%26SS..78..199B"><i>A diffraction limit on the gravitational lens effect</i> (Bontz, R. J. and Haugan, M. P. "Astrophysics and Space Science" vol. 78, no. 1, p. 199-210. August 1981)</a></li></ul> <dl><dt>Further reading</dt></dl> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBlandford_&_NarayanNarayan1992" class="citation journal cs1">Blandford & Narayan; Narayan, R (1992). "Cosmological applications of gravitational lensing". <i>Annual Review of Astronomy and Astrophysics</i>. <b>30</b> (1): 311–358. <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/1992ARA&A..30..311B">1992ARA&A..30..311B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1146%2Fannurev.aa.30.090192.001523">10.1146/annurev.aa.30.090192.001523</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annual+Review+of+Astronomy+and+Astrophysics&rft.atitle=Cosmological+applications+of+gravitational+lensing&rft.volume=30&rft.issue=1&rft.pages=311-358&rft.date=1992&rft_id=info%3Adoi%2F10.1146%2Fannurev.aa.30.090192.001523&rft_id=info%3Abibcode%2F1992ARA%26A..30..311B&rft.au=Blandford+%26+Narayan&rft.au=Narayan%2C+R&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMatthias_BartelmannPeter_Schneider2000" class="citation journal cs1">Matthias Bartelmann; Peter Schneider (2000-08-17). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070226035150/http://www.mpa-garching.mpg.de/Lenses/WLRevEls.pdf">"Weak Gravitational Lensing"</a> <span class="cs1-format">(PDF)</span>. Archived from <a rel="nofollow" class="external text" href="http://www.mpa-garching.mpg.de/Lenses/WLRevEls.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2007-02-26.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Weak+Gravitational+Lensing&rft.date=2000-08-17&rft.au=Matthias+Bartelmann&rft.au=Peter+Schneider&rft_id=http%3A%2F%2Fwww.mpa-garching.mpg.de%2FLenses%2FWLRevEls.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_journal" title="Template:Cite journal">cite journal</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Cite journal requires <code class="cs1-code">|journal=</code> (<a href="/wiki/Help:CS1_errors#missing_periodical" title="Help:CS1 errors">help</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKhavinsonNeumann2008" class="citation journal cs1">Khavinson, Dmitry; Neumann, Genevra (June–July 2008). <a rel="nofollow" class="external text" href="https://www.ams.org/notices/200806/tx080600666p.pdf">"From Fundamental Theorem of Algebra to Astrophysics: A "Harmonious" Path"</a> <span class="cs1-format">(PDF)</span>. <i>Notices of the AMS</i>. <b>55</b> (6): 666–675. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080907121928/http://www.ams.org/notices/200806/tx080600666p.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2008-09-07.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Notices+of+the+AMS&rft.atitle=From+Fundamental+Theorem+of+Algebra+to+Astrophysics%3A+A+%22Harmonious%22+Path&rft.volume=55&rft.issue=6&rft.pages=666-675&rft.date=2008-06%2F2008-07&rft.aulast=Khavinson&rft.aufirst=Dmitry&rft.au=Neumann%2C+Genevra&rft_id=https%3A%2F%2Fwww.ams.org%2Fnotices%2F200806%2Ftx080600666p.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" class="Z3988"></span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPettersLevineWambsganss2001" class="citation book cs1"><a href="/wiki/Arlie_Petters" title="Arlie Petters">Petters, Arlie O.</a>; Levine, Harold; Wambsganss, Joachim (2001). <a rel="nofollow" class="external text" href="https://www.springer.com/birkhauser/physics/book/978-0-8176-3668-5"><i>Singularity Theory and Gravitational Lensing</i></a>. Progress in Mathematical Physics. Vol. 21. Birkhäuser.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Singularity+Theory+and+Gravitational+Lensing&rft.series=Progress+in+Mathematical+Physics&rft.pub=Birkh%C3%A4user&rft.date=2001&rft.aulast=Petters&rft.aufirst=Arlie+O.&rft.au=Levine%2C+Harold&rft.au=Wambsganss%2C+Joachim&rft_id=https%3A%2F%2Fwww.springer.com%2Fbirkhauser%2Fphysics%2Fbook%2F978-0-8176-3668-5&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravitational+lens" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="http://www.matnat.uio.no/proveforelesninger/g-i/haugan-stein-vidar-hagfors.xml"><i>Tools for the evaluation of the possibilities of using parallax measurements of gravitationally lensed sources</i> (Stein Vidar Hagfors Haugan. June 2008)</a></li></ul> <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=Gravitational_lens&action=edit&section=12" 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 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.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="Relativity" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2" 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:Relativity" title="Template:Relativity"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Relativity" title="Template talk:Relativity"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Relativity" title="Special:EditPage/Template:Relativity"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Relativity" style="font-size:114%;margin:0 4em"><a href="/wiki/Theory_of_relativity" title="Theory of relativity">Relativity</a></div></th></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Special_relativity" title="Special relativity">Special<br />relativity</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Background</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Principle_of_relativity" title="Principle of relativity">Principle of relativity</a> (<a href="/wiki/Galilean_invariance" title="Galilean invariance">Galilean relativity</a></li> <li><a href="/wiki/Galilean_transformation" title="Galilean transformation">Galilean transformation</a>)</li> <li><a href="/wiki/Special_relativity" title="Special relativity">Special relativity</a></li> <li><a href="/wiki/Doubly_special_relativity" title="Doubly special relativity">Doubly special relativity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Fundamental<br />concepts</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Frame_of_reference" title="Frame of reference">Frame of reference</a></li> <li><a href="/wiki/Speed_of_light" title="Speed of light">Speed of light</a></li> <li><a href="/wiki/Hyperbolic_orthogonality" title="Hyperbolic orthogonality">Hyperbolic orthogonality</a></li> <li><a href="/wiki/Rapidity" title="Rapidity">Rapidity</a></li> <li><a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell's equations</a></li> <li><a href="/wiki/Proper_length" title="Proper length">Proper length</a></li> <li><a href="/wiki/Proper_time" title="Proper time">Proper time</a></li> <li><a href="/wiki/Proper_acceleration" title="Proper acceleration">Proper acceleration</a></li> <li><a href="/wiki/Mass_in_special_relativity" title="Mass in special relativity">Relativistic mass</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Formulation</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Lorentz_transformation" title="Lorentz transformation">Lorentz transformation</a></li> <li><a href="/wiki/List_of_textbooks_on_relativity" title="List of textbooks on relativity">Textbooks</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Phenomena</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Time_dilation" title="Time dilation">Time dilation</a></li> <li><a href="/wiki/Mass%E2%80%93energy_equivalence" title="Mass–energy equivalence">Mass–energy equivalence (E=mc<sup>2</sup>)</a></li> <li><a href="/wiki/Length_contraction" title="Length contraction">Length contraction</a></li> <li><a href="/wiki/Relativity_of_simultaneity" title="Relativity of simultaneity">Relativity of simultaneity</a></li> <li><a href="/wiki/Relativistic_Doppler_effect" title="Relativistic Doppler effect">Relativistic Doppler effect</a></li> <li><a href="/wiki/Thomas_precession" title="Thomas precession">Thomas precession</a></li> <li><a href="/wiki/Ladder_paradox" title="Ladder paradox">Ladder paradox</a></li> <li><a href="/wiki/Twin_paradox" title="Twin paradox">Twin paradox</a></li> <li><a href="/wiki/Terrell_rotation" title="Terrell rotation">Terrell rotation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;"><a href="/wiki/Spacetime" title="Spacetime">Spacetime</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Light_cone" title="Light cone">Light cone</a></li> <li><a href="/wiki/World_line" title="World line">World line</a></li> <li><a href="/wiki/Minkowski_diagram" class="mw-redirect" title="Minkowski diagram">Minkowski diagram</a></li> <li><a href="/wiki/Biquaternion" title="Biquaternion">Biquaternions</a></li> <li><a href="/wiki/Minkowski_space" title="Minkowski space">Minkowski space</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/General_relativity" title="General relativity">General<br />relativity</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Background</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Introduction_to_general_relativity" title="Introduction to general relativity">Introduction</a></li> <li><a href="/wiki/Mathematics_of_general_relativity" title="Mathematics of general relativity">Mathematical formulation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Fundamental<br />concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Equivalence_principle" title="Equivalence principle">Equivalence principle</a></li> <li><a href="/wiki/Riemannian_geometry" title="Riemannian geometry">Riemannian geometry</a></li> <li><a href="/wiki/Penrose_diagram" title="Penrose diagram">Penrose diagram</a></li> <li><a href="/wiki/Geodesics_in_general_relativity" title="Geodesics in general relativity">Geodesics</a></li> <li><a href="/wiki/Mach%27s_principle" title="Mach's principle">Mach's principle</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Formulation</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/ADM_formalism" title="ADM formalism">ADM formalism</a></li> <li><a href="/wiki/BSSN_formalism" title="BSSN formalism">BSSN formalism</a></li> <li><a href="/wiki/Einstein_field_equations" title="Einstein field equations">Einstein field equations</a></li> <li><a href="/wiki/Linearized_gravity" title="Linearized gravity">Linearized gravity</a></li> <li><a href="/wiki/Parameterized_post-Newtonian_formalism" title="Parameterized post-Newtonian formalism">Post-Newtonian formalism</a></li> <li><a href="/wiki/Raychaudhuri_equation" title="Raychaudhuri equation">Raychaudhuri equation</a></li> <li><a href="/wiki/Hamilton%E2%80%93Jacobi%E2%80%93Einstein_equation" title="Hamilton–Jacobi–Einstein equation">Hamilton–Jacobi–Einstein equation</a></li> <li><a href="/wiki/Ernst_equation" title="Ernst equation">Ernst equation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Phenomena</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Black_hole" title="Black hole">Black hole</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/Two-body_problem_in_general_relativity" title="Two-body problem in general relativity">Two-body problem</a></li></ul> <ul><li><a href="/wiki/Gravitational_wave" title="Gravitational wave">Gravitational waves</a>: <a href="/wiki/Gravitational-wave_astronomy" title="Gravitational-wave astronomy">astronomy</a></li> <li><a href="/wiki/Gravitational-wave_observatory" title="Gravitational-wave observatory">detectors</a> (<a href="/wiki/LIGO" title="LIGO">LIGO</a> and <a href="/wiki/LIGO_Scientific_Collaboration" title="LIGO Scientific Collaboration">collaboration</a></li> <li><a href="/wiki/Virgo_interferometer" title="Virgo interferometer">Virgo</a></li> <li><a href="/wiki/LISA_Pathfinder" title="LISA Pathfinder">LISA Pathfinder</a></li> <li><a href="/wiki/GEO600" title="GEO600">GEO</a>)</li> <li><a href="/wiki/Hulse%E2%80%93Taylor_binary" class="mw-redirect" title="Hulse–Taylor binary">Hulse–Taylor binary</a></li></ul> <ul><li><a href="/wiki/Tests_of_general_relativity" title="Tests of general relativity">Other tests</a>: <a href="/wiki/Apsidal_precession" title="Apsidal precession">precession</a> of Mercury</li> <li><a class="mw-selflink selflink">lensing</a> (together with <a href="/wiki/Einstein_cross" class="mw-redirect" title="Einstein cross">Einstein cross</a> and <a href="/wiki/Einstein_rings" class="mw-redirect" title="Einstein rings">Einstein rings</a>)</li> <li><a href="/wiki/Gravitational_redshift" title="Gravitational redshift">redshift</a></li> <li><a href="/wiki/Shapiro_time_delay" title="Shapiro time delay">Shapiro delay</a></li> <li><a href="/wiki/Frame-dragging" title="Frame-dragging">frame-dragging</a> / <a href="/wiki/Geodetic_effect" title="Geodetic effect">geodetic effect</a> (<a href="/wiki/Lense%E2%80%93Thirring_precession" title="Lense–Thirring precession">Lense–Thirring precession</a>)</li> <li><a href="/wiki/Pulsar_timing_array" title="Pulsar timing array">pulsar timing arrays</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Advanced<br />theories</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Brans%E2%80%93Dicke_theory" title="Brans–Dicke theory">Brans–Dicke theory</a></li> <li><a href="/wiki/Kaluza%E2%80%93Klein_theory" title="Kaluza–Klein theory">Kaluza–Klein</a></li> <li><a href="/wiki/Quantum_gravity" title="Quantum gravity">Quantum gravity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;"><a href="/wiki/Exact_solutions_in_general_relativity" title="Exact solutions in general relativity">Solutions</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li>Cosmological: <a href="/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric" title="Friedmann–Lemaître–Robertson–Walker metric">Friedmann–Lemaître–Robertson–Walker</a> (<a href="/wiki/Friedmann_equations" title="Friedmann equations">Friedmann equations</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/Kasner_metric" title="Kasner metric">Kasner</a></li> <li><a href="/wiki/BKL_singularity" title="BKL singularity">BKL singularity</a></li> <li><a href="/wiki/G%C3%B6del_metric" title="Gödel metric">Gödel</a></li> <li><a href="/wiki/Milne_model" title="Milne model">Milne</a></li></ul> <ul><li>Spherical: <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/Tolman%E2%80%93Oppenheimer%E2%80%93Volkoff_equation" title="Tolman–Oppenheimer–Volkoff equation">Tolman–Oppenheimer–Volkoff equation</a>)</li> <li><a href="/wiki/Reissner%E2%80%93Nordstr%C3%B6m_metric" title="Reissner–Nordström metric">Reissner–Nordström</a></li></ul> <ul><li>Axisymmetric: <a href="/wiki/Kerr_metric" title="Kerr metric">Kerr</a> (<a href="/wiki/Kerr%E2%80%93Newman_metric" title="Kerr–Newman metric">Kerr–Newman</a>)</li> <li><a href="/wiki/Weyl%E2%88%92Lewis%E2%88%92Papapetrou_coordinates" class="mw-redirect" title="Weyl−Lewis−Papapetrou coordinates">Weyl−Lewis−Papapetrou</a></li> <li><a href="/wiki/Taub%E2%80%93NUT_space" title="Taub–NUT space">Taub–NUT</a></li> <li><a href="/wiki/Van_Stockum_dust" title="Van Stockum dust">van Stockum dust</a></li> <li><a href="/wiki/Relativistic_disk" title="Relativistic disk">discs</a></li></ul> <ul><li>Others: <a href="/wiki/Pp-wave_spacetime" title="Pp-wave spacetime">pp-wave</a></li> <li><a href="/wiki/Ozsv%C3%A1th%E2%80%93Sch%C3%BCcking_metric" title="Ozsváth–Schücking metric">Ozsváth–Schücking</a></li> <li><a href="/wiki/Alcubierre_drive" title="Alcubierre drive">Alcubierre</a></li></ul> <ul><li>In computational physics: <a href="/wiki/Numerical_relativity" title="Numerical relativity">Numerical relativity</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Scientists</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/Henri_Poincar%C3%A9" title="Henri Poincaré">Poincaré</a></li> <li><a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz</a></li> <li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/David_Hilbert" title="David Hilbert">Hilbert</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/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/Georges_Lema%C3%AEtre" title="Georges Lemaître">Lemaître</a></li> <li><a href="/wiki/Edward_Arthur_Milne" title="Edward Arthur Milne">Milne</a></li> <li><a href="/wiki/Howard_P._Robertson" title="Howard P. Robertson">Robertson</a></li> <li><a href="/wiki/Subrahmanyan_Chandrasekhar" title="Subrahmanyan Chandrasekhar">Chandrasekhar</a></li> <li><a href="/wiki/Fritz_Zwicky" title="Fritz Zwicky">Zwicky</a></li> <li><a href="/wiki/John_Archibald_Wheeler" title="John Archibald Wheeler">Wheeler</a></li> <li><a href="/wiki/Yvonne_Choquet-Bruhat" title="Yvonne Choquet-Bruhat">Choquet-Bruhat</a></li> <li><a href="/wiki/Roy_Kerr" title="Roy Kerr">Kerr</a></li> <li><a href="/wiki/Yakov_Zeldovich" title="Yakov Zeldovich">Zel'dovich</a></li> <li><a href="/wiki/Igor_Dmitriyevich_Novikov" title="Igor Dmitriyevich Novikov">Novikov</a></li> <li><a href="/wiki/J%C3%BCrgen_Ehlers" title="Jürgen Ehlers">Ehlers</a></li> <li><a href="/wiki/Robert_Geroch" title="Robert Geroch">Geroch</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/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/Hermann_Bondi" title="Hermann Bondi">Bondi</a></li> <li><a href="/wiki/Charles_W._Misner" title="Charles W. Misner">Misner</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/Rainer_Weiss" title="Rainer Weiss">Weiss</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></td></tr><tr><td class="navbox-abovebelow" colspan="2" style="text-align:center;"><div><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" 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