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class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D1%80%D1%8B%D0%BD%D1%86%D1%8B%D0%BF_%D0%BA%D0%B0%D1%81%D0%BC%D1%96%D1%87%D0%BD%D0%B0%D0%B9_%D1%86%D1%8D%D0%BD%D0%B7%D1%83%D1%80%D1%8B" title="Прынцып касмічнай цэнзуры – Belarusian" lang="be" hreflang="be" data-title="Прынцып касмічнай цэнзуры" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Hypot%C3%A9za_kosmick%C3%A9_cenzury" title="Hypotéza kosmické cenzury – Czech" lang="cs" hreflang="cs" data-title="Hypotéza kosmické cenzury" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Hip%C3%B3tesis_de_censura_c%C3%B3smica" title="Hipótesis de censura cósmica – Spanish" lang="es" hreflang="es" data-title="Hipótesis de censura cósmica" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%81%D8%B1%D8%B6%DB%8C%D9%87_%D8%B3%D8%A7%D9%86%D8%B3%D9%88%D8%B1_%DA%A9%DB%8C%D9%87%D8%A7%D9%86%DB%8C" title="فرضیه سانسور کیهانی – Persian" lang="fa" hreflang="fa" data-title="فرضیه سانسور کیهانی" 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/Censure_cosmique" title="Censure cosmique – French" lang="fr" hreflang="fr" data-title="Censure cosmique" data-language-autonym="Français" 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class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Mathematical conjecture in physics</div> <p>The weak and the strong <b>cosmic censorship hypotheses</b> are two mathematical <a href="/wiki/Conjecture" title="Conjecture">conjectures</a> about the structure of <a href="/wiki/Gravitational_singularity" title="Gravitational singularity">gravitational singularities</a> arising in <a href="/wiki/General_relativity" title="General relativity">general relativity</a>. </p><p>Singularities that arise in the <a href="/wiki/Solutions_of_the_Einstein_field_equations" title="Solutions of the Einstein field equations">solutions</a> of <a href="/wiki/Einstein%27s_field_equation" class="mw-redirect" title="Einstein's field equation">Einstein's equations</a> are typically hidden within <a href="/wiki/Event_horizon" title="Event horizon">event horizons</a>, and therefore cannot be observed from the rest of <a href="/wiki/Spacetime" title="Spacetime">spacetime</a>. Singularities that are not so hidden are called <i><a href="/wiki/Naked_singularity" title="Naked singularity">naked</a></i>. The <b>weak cosmic censorship hypothesis</b> was conceived by <a href="/wiki/Roger_Penrose" title="Roger Penrose">Roger Penrose</a> in 1969 and posits that no naked singularities exist in the <a href="/wiki/Universe" title="Universe">universe</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Basics">Basics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_censorship_hypothesis&action=edit&section=1" title="Edit section: Basics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Since the physical behavior of singularities is unknown, if singularities can be observed from the rest of spacetime, <a href="/wiki/Causality" title="Causality">causality</a> may break down, and <a href="/wiki/Physics" title="Physics">physics</a> may lose its predictive power. The issue cannot be avoided, since according to the <a href="/wiki/Penrose%E2%80%93Hawking_singularity_theorems" title="Penrose–Hawking singularity theorems">Penrose–Hawking singularity theorems</a>, singularities are inevitable in physically reasonable situations. Still, in the absence of naked singularities, the universe, as described by the <a href="/wiki/General_theory_of_relativity" class="mw-redirect" title="General theory of relativity">general theory of relativity</a>, is <a href="/wiki/Determinism" title="Determinism">deterministic</a>:<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> it is possible to predict the entire evolution of the universe (possibly excluding some finite regions of space hidden inside event horizons of singularities), knowing only its condition at a certain moment of time (more precisely, everywhere on a <a href="/wiki/Spacelike" class="mw-redirect" title="Spacelike">spacelike</a> three-dimensional hypersurface, called the <a href="/wiki/Cauchy_surface" title="Cauchy surface">Cauchy surface</a>). Failure of the cosmic censorship hypothesis leads to the failure of determinism, because it is yet impossible to predict the behavior of spacetime in the causal future of a singularity. Cosmic censorship is not merely a problem of formal interest; some form of it is assumed whenever <a href="/wiki/Black_hole" title="Black hole">black hole</a> event horizons are mentioned.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (October 2015)">citation needed</span></a></i>]</sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Roger_Penrose-6Nov2005.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Roger_Penrose-6Nov2005.jpg/220px-Roger_Penrose-6Nov2005.jpg" decoding="async" width="220" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Roger_Penrose-6Nov2005.jpg/330px-Roger_Penrose-6Nov2005.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Roger_Penrose-6Nov2005.jpg/440px-Roger_Penrose-6Nov2005.jpg 2x" data-file-width="1024" data-file-height="683" /></a><figcaption>Roger Penrose first formulated the cosmic censorship hypothesis in 1969.</figcaption></figure> <p>The hypothesis was first formulated by <a href="/wiki/Roger_Penrose" title="Roger Penrose">Roger Penrose</a> in 1969,<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> and it is not stated in a completely formal way. In a sense it is more of a research program proposal: part of the research is to find a proper formal statement that is physically reasonable, <a href="/wiki/Falsifiable" class="mw-redirect" title="Falsifiable">falsifiable</a>, and sufficiently general to be interesting.<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> Because the statement is not a strictly formal one, there is sufficient latitude for (at least) two independent formulations: a weak form, and a strong form. </p> <div class="mw-heading mw-heading2"><h2 id="Weak_and_strong_cosmic_censorship_hypothesis">Weak and strong cosmic censorship hypothesis</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_censorship_hypothesis&action=edit&section=2" title="Edit section: Weak and strong cosmic censorship hypothesis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The weak and the strong cosmic censorship hypotheses are two conjectures concerned with the global geometry of spacetimes. </p><p>The <b>weak cosmic censorship hypothesis</b> asserts there can be no singularity visible from future <a href="/wiki/Null_infinity" title="Null infinity">null infinity</a>. In other words, singularities need to be hidden from an observer at infinity by the event horizon of a <a href="/wiki/Black_hole" title="Black hole">black hole</a>. Mathematically, the conjecture states that, for generic initial data, the <a href="/wiki/Causal_structure" title="Causal structure">causal structure</a> is such that the maximal <a href="/wiki/Cauchy_surface" title="Cauchy surface">Cauchy development</a> possesses a complete future null infinity. </p><p>The <b>strong cosmic censorship hypothesis</b> asserts that, generically, general relativity is a deterministic theory, in the same sense that classical mechanics is a deterministic theory. In other words, the classical fate of all observers should be predictable from the initial data. Mathematically, the conjecture states that the maximal Cauchy development of generic compact or asymptotically flat initial data is locally inextendible as a regular <a href="/wiki/Lorentzian_manifold" class="mw-redirect" title="Lorentzian manifold">Lorentzian manifold</a>. Taken in its strongest sense, the conjecture suggests locally inextendibility of the maximal Cauchy development as a continuous Lorentzian manifold [very Strong Cosmic Censorship]. This strongest version was disproven in 2018 by Mihalis Dafermos and Jonathan Luk for the <a href="/wiki/Cauchy_horizon" title="Cauchy horizon">Cauchy horizon</a> of an <a href="/wiki/Kerr_metric" title="Kerr metric">uncharged, rotating black hole</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>The two conjectures are mathematically independent, as there exist spacetimes for which weak cosmic censorship is valid but strong cosmic censorship is violated and, conversely, there exist spacetimes for which weak cosmic censorship is violated but strong cosmic censorship is valid. </p> <div class="mw-heading mw-heading2"><h2 id="Example">Example</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_censorship_hypothesis&action=edit&section=3" title="Edit section: Example"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Kerr_metric" title="Kerr metric">Kerr metric</a>, corresponding to a black hole 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> and angular momentum <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 J}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/359e4f407b49910e02c27c2f52e87a36cd74c053" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.471ex; height:2.176ex;" alt="{\displaystyle J}"></span>, can be used to derive the <a href="/wiki/Effective_potential" title="Effective potential">effective potential</a> for particle <a href="/wiki/Orbits" class="mw-redirect" title="Orbits">orbits</a> restricted to the equator (as defined by rotation). This potential looks like:<sup id="cite_ref-hartle_gravity_5-0" class="reference"><a href="#cite_note-hartle_gravity-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\rm {eff}}(r,e,\ell )=-{\frac {M}{r}}+{\frac {\ell ^{2}-a^{2}(e^{2}-1)}{2r^{2}}}-{\frac {M(\ell -ae)^{2}}{r^{3}}},~~~a\equiv {\frac {J}{M}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> <mo stretchy="false">(</mo> <mi>r</mi> <mo>,</mo> <mi>e</mi> <mo>,</mo> <mi>ℓ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>M</mi> <mi>r</mi> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mrow> <mn>2</mn> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>M</mi> <mo stretchy="false">(</mo> <mi>ℓ</mi> <mo>−</mo> <mi>a</mi> <mi>e</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mfrac> </mrow> <mo>,</mo> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mi>a</mi> <mo>≡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>J</mi> <mi>M</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\rm {eff}}(r,e,\ell )=-{\frac {M}{r}}+{\frac {\ell ^{2}-a^{2}(e^{2}-1)}{2r^{2}}}-{\frac {M(\ell -ae)^{2}}{r^{3}}},~~~a\equiv {\frac {J}{M}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84032ab6408bafc107a7cefbff84d470c0f374b9" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:62.968ex; height:6.176ex;" alt="{\displaystyle V_{\rm {eff}}(r,e,\ell )=-{\frac {M}{r}}+{\frac {\ell ^{2}-a^{2}(e^{2}-1)}{2r^{2}}}-{\frac {M(\ell -ae)^{2}}{r^{3}}},~~~a\equiv {\frac {J}{M}}}"></span> 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 coordinate radius, <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 e}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd253103f0876afc68ebead27a5aa9867d927467" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle e}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ell }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ℓ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ell }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f066e981e530bacc07efc6a10fa82deee985929e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.97ex; height:2.176ex;" alt="{\displaystyle \ell }"></span> are the test-particle's conserved energy and angular momentum respectively (constructed from the <a href="/wiki/Killing_vectors" class="mw-redirect" title="Killing vectors">Killing vectors</a>). </p><p>To preserve <i>cosmic censorship</i>, the black hole is restricted to the case of <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 a<1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo><</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a<1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b8d3f65a187e46328021b646ee8769425a04d72" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.491ex; height:2.176ex;" alt="{\displaystyle a<1}"></span>. For there to exist an <a href="/wiki/Event_horizon" title="Event horizon">event horizon</a> around the singularity, the requirement <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 a<1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo><</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a<1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b8d3f65a187e46328021b646ee8769425a04d72" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.491ex; height:2.176ex;" alt="{\displaystyle a<1}"></span> must be satisfied.<sup id="cite_ref-hartle_gravity_5-1" class="reference"><a href="#cite_note-hartle_gravity-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> This amounts to the <a href="/wiki/Angular_momentum" title="Angular momentum">angular momentum</a> of the black hole being constrained to below a critical value, outside of which the horizon would disappear. </p><p>The following thought experiment is reproduced from Hartle's <i>Gravity</i>: </p> <p><span class="anchor" id="Violating_cosmic_censorship"></span><style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style></p><blockquote class="templatequote"><p>Imagine specifically trying to violate the censorship conjecture. This could be done by somehow imparting an angular momentum upon the black hole, making it exceed the critical value (assume it starts infinitesimally below it). This could be done by sending a particle of angular momentum <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 \ell =2Me}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ℓ</mi> <mo>=</mo> <mn>2</mn> <mi>M</mi> <mi>e</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ell =2Me}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c536b97512b43a4e6558a0751ecec431770a5ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.756ex; height:2.176ex;" alt="{\displaystyle \ell =2Me}"></span>. Because this particle has angular momentum, it can only be captured by the black hole if the maximum potential of the black hole is less than <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 (e^{2}-1)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (e^{2}-1)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4c442d5a2766b177b3bb83bb69af4812d22f009" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.275ex; height:3.176ex;" alt="{\displaystyle (e^{2}-1)/2}"></span>.<br /> Solving the above effective potential equation for the maximum under the given conditions results in a maximum potential of exactly <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 (e^{2}-1)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (e^{2}-1)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4c442d5a2766b177b3bb83bb69af4812d22f009" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.275ex; height:3.176ex;" alt="{\displaystyle (e^{2}-1)/2}"></span>. Testing other values shows that no particle with enough angular momentum to violate the censorship conjecture would be able to enter the black hole, <i>because</i> they have too much angular momentum to fall in.</p></blockquote> <div class="mw-heading mw-heading2"><h2 id="Problems_with_the_concept">Problems with the concept</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_censorship_hypothesis&action=edit&section=4" title="Edit section: Problems with the concept"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There are a number of difficulties in formalizing the hypothesis: </p> <ul><li>There are technical difficulties with properly formalizing the notion of a singularity.</li> <li>It is not difficult to construct spacetimes which have naked singularities, but which are not "physically reasonable"; the canonical example of such a spacetime is perhaps the "superextremal" <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<|Q|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo><</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M<|Q|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2895353062aa168c21c71141d0c45c45cb14b280" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.673ex; height:2.843ex;" alt="{\displaystyle M<|Q|}"></span> <a href="/wiki/Reissner%E2%80%93Nordstr%C3%B6m" class="mw-redirect" title="Reissner–Nordström">Reissner–Nordström</a> solution, which contains a singularity at <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=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/894a83e863728b4ee2e12f3a999a09f5f2bf1c89" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.31ex; height:2.176ex;" alt="{\displaystyle r=0}"></span> that is not surrounded by a horizon. A formal statement needs some set of hypotheses which exclude these situations.</li> <li><a href="/wiki/Caustic_(mathematics)" title="Caustic (mathematics)">Caustics</a> may occur in simple models of <a href="/wiki/Gravitational_collapse" title="Gravitational collapse">gravitational collapse</a>, and can appear to lead to singularities. These have more to do with the simplified models of bulk matter used, and in any case have nothing to do with general relativity, and need to be excluded.</li> <li>Computer models of gravitational collapse have shown that naked singularities can arise, but these models rely on very special circumstances (such as spherical symmetry). These special circumstances need to be excluded by some hypotheses.</li></ul> <p>In 1991, <a href="/wiki/John_Preskill" title="John Preskill">John Preskill</a> and <a href="/wiki/Kip_Thorne" title="Kip Thorne">Kip Thorne</a> <a href="/wiki/Scientific_wager" title="Scientific wager">bet against</a> <a href="/wiki/Stephen_Hawking" title="Stephen Hawking">Stephen Hawking</a> that the hypothesis was false. Hawking conceded the bet in 1997, due to the discovery of the special situations just mentioned, which he characterized as "technicalities". Hawking later reformulated the bet to exclude those technicalities. The revised bet is still open (although Hawking died in 2018), the prize being "clothing to cover the winner's nakedness".<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> <div class="mw-heading mw-heading2"><h2 id="Counter-example">Counter-example</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_censorship_hypothesis&action=edit&section=5" title="Edit section: Counter-example"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An exact solution to the scalar-Einstein equations <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_{ab}=2\phi _{a}\phi _{b}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mn>2</mn> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{ab}=2\phi _{a}\phi _{b}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7ddc13d1c22d30ded07e0313707c29f4624cc2b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.643ex; height:2.509ex;" alt="{\displaystyle R_{ab}=2\phi _{a}\phi _{b}}"></span> which forms a counterexample to many formulations of the cosmic censorship hypothesis was found by Mark D. Roberts in 1985: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ds^{2}=-(1+2\sigma )\,dv^{2}+2\,dv\,dr+r(r-2\sigma v)\left(d\theta ^{2}+\sin ^{2}\theta \,d\phi ^{2}\right),\quad \varphi ={\frac {1}{2}}\ln \left(1-{\frac {2\sigma v}{r}}\right),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo>−</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mn>2</mn> <mi>σ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mspace width="thinmathspace" /> <mi>d</mi> <mi>v</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>r</mi> <mo>+</mo> <mi>r</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo>−</mo> <mn>2</mn> <mi>σ</mi> <mi>v</mi> <mo stretchy="false">)</mo> <mrow> <mo>(</mo> <mrow> <mi>d</mi> <msup> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>θ</mi> <mspace width="thinmathspace" /> <mi>d</mi> <msup> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mspace width="1em" /> <mi>φ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ln</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>σ</mi> <mi>v</mi> </mrow> <mi>r</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ds^{2}=-(1+2\sigma )\,dv^{2}+2\,dv\,dr+r(r-2\sigma v)\left(d\theta ^{2}+\sin ^{2}\theta \,d\phi ^{2}\right),\quad \varphi ={\frac {1}{2}}\ln \left(1-{\frac {2\sigma v}{r}}\right),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54437028201af3e8b7995deef9872f62f363c5ac" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:86.31ex; height:6.176ex;" alt="{\displaystyle ds^{2}=-(1+2\sigma )\,dv^{2}+2\,dv\,dr+r(r-2\sigma v)\left(d\theta ^{2}+\sin ^{2}\theta \,d\phi ^{2}\right),\quad \varphi ={\frac {1}{2}}\ln \left(1-{\frac {2\sigma v}{r}}\right),}"></span> 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 \sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f59b7c3e6fdb1d0365a494b81fb9a696138c36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle \sigma }"></span> is a constant.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_censorship_hypothesis&action=edit&section=6" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239009302">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px 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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="CITEREFEarman2007" class="citation book cs1">Earman, J. (2007). <a rel="nofollow" class="external text" href="https://sites.socsci.uci.edu/~dmalamen/courses/prob-determ/Earman.pdf">"Aspects of Determinism in Modern Physics"</a> <span class="cs1-format">(PDF)</span>. In Gabbay, Dov M.; Thagard, Paul; Woods, John (eds.). <i>Handbook of the philosophy of science</i>. Amsterdam: <a href="/wiki/Elsevier" title="Elsevier">Elsevier</a>. pp. 1369–1434. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-444-51560-5" title="Special:BookSources/978-0-444-51560-5"><bdi>978-0-444-51560-5</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140522160538/http://www.pitt.edu/~jearman/Earman2007a.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2014-05-22.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Aspects+of+Determinism+in+Modern+Physics&rft.btitle=Handbook+of+the+philosophy+of+science&rft.place=Amsterdam&rft.pages=1369-1434&rft.pub=Elsevier&rft.date=2007&rft.isbn=978-0-444-51560-5&rft.aulast=Earman&rft.aufirst=J.&rft_id=https%3A%2F%2Fsites.socsci.uci.edu%2F~dmalamen%2Fcourses%2Fprob-determ%2FEarman.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACosmic+censorship+hypothesis" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPenrose1969" class="citation journal cs1">Penrose, Roger (1969). 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(February 12, 1997). <a rel="nofollow" class="external text" href="https://www.nytimes.com/1997/02/12/us/a-bet-on-a-cosmic-scale-and-a-concession-sort-of.html">"A Bet on a Cosmic Scale, And a Concession, Sort Of"</a>. <i><a href="/wiki/The_New_York_Times" title="The New York Times">The New York Times</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+New+York+Times&rft.atitle=A+Bet+on+a+Cosmic+Scale%2C+And+a+Concession%2C+Sort+Of&rft.date=1997-02-12&rft.aulast=Browne&rft.aufirst=Malcom+W.&rft_id=https%3A%2F%2Fwww.nytimes.com%2F1997%2F02%2F12%2Fus%2Fa-bet-on-a-cosmic-scale-and-a-concession-sort-of.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACosmic+censorship+hypothesis" 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="CITEREFHartnett2018" class="citation magazine cs1">Hartnett, Kevin (17 May 2018). <a rel="nofollow" class="external text" href="https://www.quantamagazine.org/mathematicians-disprove-conjecture-made-to-save-black-holes-20180517/">"Mathematicians Disprove Conjecture Made to Save Black Holes"</a>. <i><a href="/wiki/Quanta_Magazine" title="Quanta Magazine">Quanta Magazine</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">29 March</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Quanta+Magazine&rft.atitle=Mathematicians+Disprove+Conjecture+Made+to+Save+Black+Holes&rft.date=2018-05-17&rft.aulast=Hartnett&rft.aufirst=Kevin&rft_id=https%3A%2F%2Fwww.quantamagazine.org%2Fmathematicians-disprove-conjecture-made-to-save-black-holes-20180517%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACosmic+censorship+hypothesis" class="Z3988"></span></span> </li> <li id="cite_note-hartle_gravity-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-hartle_gravity_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-hartle_gravity_5-1"><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="CITEREFHartle2003" class="citation book cs1">Hartle, J. B. (2003). 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San Francisco: <a href="/wiki/Addison-Wesley" title="Addison-Wesley">Addison-Wesley</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8053-8662-2" title="Special:BookSources/978-0-8053-8662-2"><bdi>978-0-8053-8662-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=15%3A+Rotating+Black+Holes&rft.btitle=Gravity%3A+an+introduction+to+Einstein%27s+general+relativity&rft.place=San+Francisco&rft.pub=Addison-Wesley&rft.date=2003&rft.isbn=978-0-8053-8662-2&rft.aulast=Hartle&rft.aufirst=J.+B.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACosmic+censorship+hypothesis" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20040606135525/http://www.theory.caltech.edu/people/preskill/new_naked_bet.html">"New bet on naked singularities"</a>. 5 February 1997. Archived from <a rel="nofollow" class="external text" href="http://www.theory.caltech.edu/people/preskill/new_naked_bet.html">the original</a> on 6 June 2004.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=New+bet+on+naked+singularities&rft.date=1997-02-05&rft_id=http%3A%2F%2Fwww.theory.caltech.edu%2Fpeople%2Fpreskill%2Fnew_naked_bet.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACosmic+censorship+hypothesis" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRoberts1989" class="citation journal cs1">Roberts, M. D. (September 1989). "Scalar field counterexamples to the cosmic censorship hypothesis". <i>General Relativity and Gravitation</i>. <b>21</b> (9). Springer Science and Business Media LLC: 907–939. <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/1989GReGr..21..907R">1989GReGr..21..907R</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%2FBF00769864">10.1007/BF00769864</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0001-7701">0001-7701</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:121601921">121601921</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=General+Relativity+and+Gravitation&rft.atitle=Scalar+field+counterexamples+to+the+cosmic+censorship+hypothesis&rft.volume=21&rft.issue=9&rft.pages=907-939&rft.date=1989-09&rft_id=info%3Adoi%2F10.1007%2FBF00769864&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A121601921%23id-name%3DS2CID&rft.issn=0001-7701&rft_id=info%3Abibcode%2F1989GReGr..21..907R&rft.aulast=Roberts&rft.aufirst=M.+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACosmic+censorship+hypothesis" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_censorship_hypothesis&action=edit&section=8" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEarman1995" class="citation book cs1">Earman, John (1995). <a rel="nofollow" class="external text" href="https://sites.pitt.edu/~jearman/Earman_1995BangsCrunches.pdf"><i>Bangs, crunches, whimpers, and shrieks: singularities and acausalities in relativistic spacetimes</i></a> <span class="cs1-format">(PDF)</span>. New York: <a href="/wiki/Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>. See especially chapter 2. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-509591-3" title="Special:BookSources/978-0-19-509591-3"><bdi>978-0-19-509591-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Bangs%2C+crunches%2C+whimpers%2C+and+shrieks%3A+singularities+and+acausalities+in+relativistic+spacetimes&rft.place=New+York&rft.pages=See+especially+chapter+2&rft.pub=Oxford+University+Press&rft.date=1995&rft.isbn=978-0-19-509591-3&rft.aulast=Earman&rft.aufirst=John&rft_id=https%3A%2F%2Fsites.pitt.edu%2F~jearman%2FEarman_1995BangsCrunches.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACosmic+censorship+hypothesis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWald1998" class="citation book cs1">Wald, Robert M. (1998). "The Question of Cosmic Censorship". In Wald, Robert M. (ed.). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/blackholesrelati0000unse"><i>Black holes and relativistic stars</i></a></span>. Chicago: <a href="/wiki/University_of_Chicago_Press" title="University of Chicago Press">University of Chicago Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-226-87034-2" title="Special:BookSources/978-0-226-87034-2"><bdi>978-0-226-87034-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Question+of+Cosmic+Censorship&rft.btitle=Black+holes+and+relativistic+stars&rft.place=Chicago&rft.pub=University+of+Chicago+Press&rft.date=1998&rft.isbn=978-0-226-87034-2&rft.aulast=Wald&rft.aufirst=Robert+M.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fblackholesrelati0000unse&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACosmic+censorship+hypothesis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPenrose1979" class="citation book cs1">Penrose, Roger (1979). "Singularities and time-asymmetry". In Hawking, Stephen; Israel, W. (eds.). <i>General relativity: an Einstein centenary survey</i>. Cambridge [Eng.] ; New York: <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. See especially section 12.3.2, pp. 617–629. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-22285-3" title="Special:BookSources/978-0-521-22285-3"><bdi>978-0-521-22285-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Singularities+and+time-asymmetry&rft.btitle=General+relativity%3A+an+Einstein+centenary+survey&rft.place=Cambridge+%5BEng.%5D+%3B+New+York&rft.pages=See+especially+section+12.3.2%2C+pp.-617-629&rft.pub=Cambridge+University+Press&rft.date=1979&rft.isbn=978-0-521-22285-3&rft.aulast=Penrose&rft.aufirst=Roger&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACosmic+censorship+hypothesis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShapiroTeukolsky1991" class="citation journal cs1">Shapiro, Stuart L.; Teukolsky, Saul A. (25 February 1991). <a rel="nofollow" class="external text" href="https://authors.library.caltech.edu/87494/1/PhysRevLett.66.994.pdf">"Formation of naked singularities: The violation of cosmic censorship"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/Physical_Review_Letters" title="Physical Review Letters">Physical Review Letters</a></i>. <b>66</b> (8). <a href="/wiki/American_Physical_Society" title="American Physical Society">American Physical Society</a> (APS): 994–997. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1991PhRvL..66..994S">1991PhRvL..66..994S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.66.994">10.1103/PhysRevLett.66.994</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0031-9007">0031-9007</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/10043968">10043968</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:7830407">7830407</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20191205090055/https://authors.library.caltech.edu/87494/1/PhysRevLett.66.994.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2019-12-05.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Formation+of+naked+singularities%3A+The+violation+of+cosmic+censorship&rft.volume=66&rft.issue=8&rft.pages=994-997&rft.date=1991-02-25&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A7830407%23id-name%3DS2CID&rft_id=info%3Abibcode%2F1991PhRvL..66..994S&rft.issn=0031-9007&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.66.994&rft_id=info%3Apmid%2F10043968&rft.aulast=Shapiro&rft.aufirst=Stuart+L.&rft.au=Teukolsky%2C+Saul+A.&rft_id=https%3A%2F%2Fauthors.library.caltech.edu%2F87494%2F1%2FPhysRevLett.66.994.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACosmic+censorship+hypothesis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWald1984" class="citation book cs1">Wald, Robert M. (1984). <a rel="nofollow" class="external text" href="https://fma.if.usp.br/~mlima/teaching/PGF5292_2021/Wald_GR.pdf"><i>General relativity</i></a> <span class="cs1-format">(PDF)</span>. Chicago: <a href="/wiki/University_of_Chicago_Press" title="University of Chicago Press">University of Chicago Press</a>. pp. 299–308. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-226-87032-8" title="Special:BookSources/978-0-226-87032-8"><bdi>978-0-226-87032-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=General+relativity&rft.place=Chicago&rft.pages=299-308&rft.pub=University+of+Chicago+Press&rft.date=1984&rft.isbn=978-0-226-87032-8&rft.aulast=Wald&rft.aufirst=Robert+M.&rft_id=https%3A%2F%2Ffma.if.usp.br%2F~mlima%2Fteaching%2FPGF5292_2021%2FWald_GR.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACosmic+censorship+hypothesis" class="Z3988"></span></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=Cosmic_censorship_hypothesis&action=edit&section=9" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20051217081439/http://www.theory.caltech.edu/people/preskill/old_naked_bet.html">The old bet</a> (conceded in 1997)</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20040606135525/http://www.theory.caltech.edu/people/preskill/new_naked_bet.html">The new bet</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output 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template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Black_holes" title="Template talk:Black holes"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Black_holes" title="Special:EditPage/Template:Black holes"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Black_holes" style="font-size:114%;margin:0 4em"><a href="/wiki/Black_hole" title="Black hole">Black holes</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="3" style="text-align:center;"><div> <ul><li><a href="/wiki/Outline_of_black_holes" title="Outline of black holes">Outline</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Types</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/BTZ_black_hole" title="BTZ black hole">BTZ black hole</a></li> <li><a href="/wiki/Schwarzschild_metric" title="Schwarzschild metric">Schwarzschild</a></li> <li><a href="/wiki/Rotating_black_hole" title="Rotating black hole">Rotating</a></li> <li><a href="/wiki/Charged_black_hole" title="Charged black hole">Charged</a></li> <li><a href="/wiki/Virtual_black_hole" title="Virtual black hole">Virtual</a></li> <li><a href="/wiki/Kugelblitz_(astrophysics)" title="Kugelblitz (astrophysics)">Kugelblitz</a></li> <li><a href="/wiki/Supermassive_black_hole" title="Supermassive black hole">Supermassive</a></li> <li><a href="/wiki/Primordial_black_hole" title="Primordial black hole">Primordial</a></li> <li><a href="/wiki/Direct_collapse_black_hole" title="Direct collapse black hole">Direct collapse</a></li> <li><a href="/wiki/Rogue_black_hole" title="Rogue black hole">Rogue</a></li> <li><a href="/wiki/Malament%E2%80%93Hogarth_spacetime" title="Malament–Hogarth spacetime">Malament–Hogarth spacetime</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="11" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Black_hole_-_Messier_87_crop_max_res.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Black_hole_-_Messier_87_crop_max_res.jpg/80px-Black_hole_-_Messier_87_crop_max_res.jpg" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Black_hole_-_Messier_87_crop_max_res.jpg/120px-Black_hole_-_Messier_87_crop_max_res.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Black_hole_-_Messier_87_crop_max_res.jpg/160px-Black_hole_-_Messier_87_crop_max_res.jpg 2x" data-file-width="4320" data-file-height="4320" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Size</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Micro_black_hole" title="Micro black hole">Micro</a> <ul><li><a href="/wiki/Extremal_black_hole" title="Extremal black hole">Extremal</a></li> <li><a href="/wiki/Black_hole_electron" title="Black hole electron">Electron</a></li></ul></li> <li><a href="/wiki/Stellar_black_hole" title="Stellar black hole">Stellar</a> <ul><li><a href="/wiki/Microquasar" title="Microquasar">Microquasar</a></li></ul></li> <li><a href="/wiki/Intermediate-mass_black_hole" title="Intermediate-mass black hole">Intermediate-mass</a></li> <li><a href="/wiki/Supermassive_black_hole" title="Supermassive black hole">Supermassive</a> <ul><li><a href="/wiki/Active_galactic_nucleus" title="Active galactic nucleus">Active galactic nucleus</a></li> <li><a href="/wiki/Quasar" title="Quasar">Quasar</a></li> <li><a href="/wiki/Large_quasar_group" title="Large quasar group">LQG</a></li> <li><a href="/wiki/Blazar" title="Blazar">Blazar</a></li> <li><a href="/wiki/OVV_quasar" title="OVV quasar">OVV</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Formation</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Stellar_evolution" title="Stellar evolution">Stellar evolution</a></li> <li><a href="/wiki/Gravitational_collapse" title="Gravitational collapse">Gravitational collapse</a></li> <li><a href="/wiki/Neutron_star" title="Neutron star">Neutron star</a> <ul><li><a href="/wiki/Template:Neutron_star" title="Template:Neutron star">Related links</a></li></ul></li> <li><a href="/wiki/Tolman%E2%80%93Oppenheimer%E2%80%93Volkoff_limit" title="Tolman–Oppenheimer–Volkoff limit">Tolman–Oppenheimer–Volkoff limit</a></li> <li><a href="/wiki/White_dwarf" title="White dwarf">White dwarf</a> <ul><li><a href="/wiki/Template:White_dwarf" title="Template:White dwarf">Related links</a></li></ul></li> <li><a href="/wiki/Supernova" title="Supernova">Supernova</a> <ul><li><a href="/wiki/Micronova" title="Micronova">Micronova</a></li> <li><a href="/wiki/Superluminous_supernova" title="Superluminous supernova">Hypernova</a></li> <li><a href="/wiki/Template:Supernovae" title="Template:Supernovae">Related links</a></li></ul></li> <li><a href="/wiki/Gamma-ray_burst" title="Gamma-ray burst">Gamma-ray burst</a></li> <li><a href="/wiki/Binary_black_hole" title="Binary black hole">Binary black hole</a></li> <li><a href="/wiki/Quark_star" title="Quark star">Quark star</a></li> <li><a href="/wiki/Supermassive_star" class="mw-redirect" title="Supermassive star">Supermassive star</a></li> <li><a href="/wiki/Quasi-star" title="Quasi-star">Quasi-star</a></li> <li><a href="/wiki/Dark_star_(dark_matter)" title="Dark star (dark matter)">Supermassive dark star</a></li> <li><a href="/wiki/X-ray_binary" title="X-ray binary">X-ray binary</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Properties</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Astrophysical_jet" title="Astrophysical jet">Astrophysical jet</a></li> <li><a href="/wiki/Gravitational_singularity" title="Gravitational singularity">Gravitational singularity</a> <ul><li><a href="/wiki/Ring_singularity" title="Ring singularity">Ring singularity</a></li> <li><a href="/wiki/Penrose%E2%80%93Hawking_singularity_theorems" title="Penrose–Hawking singularity theorems">Theorems</a></li></ul></li> <li><a href="/wiki/Event_horizon" title="Event horizon">Event horizon</a></li> <li><a href="/wiki/Photon_sphere" title="Photon sphere">Photon sphere</a></li> <li><a href="/wiki/Innermost_stable_circular_orbit" title="Innermost stable circular orbit">Innermost stable circular orbit</a></li> <li><a href="/wiki/Ergosphere" title="Ergosphere">Ergosphere</a> <ul><li><a href="/wiki/Penrose_process" title="Penrose process">Penrose process</a></li> <li><a href="/wiki/Blandford%E2%80%93Znajek_process" title="Blandford–Znajek process">Blandford–Znajek process</a></li></ul></li> <li><a href="/wiki/Accretion_disk" title="Accretion disk">Accretion disk</a></li> <li><a href="/wiki/Hawking_radiation" title="Hawking radiation">Hawking radiation</a></li> <li><a href="/wiki/Gravitational_lens" title="Gravitational lens">Gravitational lens</a> <ul><li><a href="/wiki/Gravitational_microlensing" title="Gravitational microlensing">Microlens</a></li></ul></li> <li><a href="/wiki/Bondi_accretion" title="Bondi accretion">Bondi accretion</a></li> <li><a href="/wiki/M%E2%80%93sigma_relation" title="M–sigma relation">M–sigma relation</a></li> <li><a href="/wiki/Quasi-periodic_oscillation" class="mw-redirect" title="Quasi-periodic oscillation">Quasi-periodic oscillation</a></li> <li><a href="/wiki/Black_hole_thermodynamics" title="Black hole thermodynamics">Thermodynamics</a></li> <li><a href="/wiki/Bekenstein_bound" title="Bekenstein bound">Bekenstein bound</a></li> <li><a href="/wiki/Bousso%27s_holographic_bound" title="Bousso's holographic bound">Bousso's holographic bound</a> <ul><li><a href="/wiki/Immirzi_parameter" title="Immirzi parameter">Immirzi parameter</a></li></ul></li> <li><a href="/wiki/Schwarzschild_radius" title="Schwarzschild radius">Schwarzschild radius</a></li> <li><a href="/wiki/Spaghettification" title="Spaghettification">Spaghettification</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Issues</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Black_hole_complementarity" title="Black hole complementarity">Black hole complementarity</a></li> <li><a href="/wiki/Black_hole_information_paradox" title="Black hole information paradox">Information paradox</a></li> <li><a class="mw-selflink selflink">Cosmic censorship</a></li> <li><a href="/wiki/ER_%3D_EPR" title="ER = EPR">ER = EPR</a></li> <li><a href="/wiki/Binary_black_hole#Final_parsec_problem" title="Binary black hole">Final parsec problem</a></li> <li><a href="/wiki/Firewall_(physics)" title="Firewall (physics)">Firewall (physics)</a></li> <li><a href="/wiki/Holographic_principle" title="Holographic principle">Holographic principle</a></li> <li><a href="/wiki/No-hair_theorem" title="No-hair theorem">No-hair theorem</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Metrics</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Schwarzschild_metric" title="Schwarzschild metric">Schwarzschild</a> (<a href="/wiki/Derivation_of_the_Schwarzschild_solution" title="Derivation of the Schwarzschild solution">Derivation</a>)</li> <li><a href="/wiki/Kerr_metric" title="Kerr metric">Kerr</a></li> <li><a href="/wiki/Reissner%E2%80%93Nordstr%C3%B6m_metric" title="Reissner–Nordström metric">Reissner–Nordström</a></li> <li><a href="/wiki/Kerr%E2%80%93Newman_metric" title="Kerr–Newman metric">Kerr–Newman</a></li> <li><a href="/wiki/Hayward_metric" title="Hayward metric">Hayward</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Alternatives</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Nonsingular_black_hole_models" title="Nonsingular black hole models">Nonsingular black hole models</a></li> <li><a href="/wiki/Black_star_(semiclassical_gravity)" title="Black star (semiclassical gravity)">Black star</a></li> <li><a href="/wiki/Dark_star_(Newtonian_mechanics)" title="Dark star (Newtonian mechanics)">Dark star</a></li> <li><a href="/wiki/Dark-energy_star" title="Dark-energy star">Dark-energy star</a></li> <li><a href="/wiki/Gravastar" title="Gravastar">Gravastar</a></li> <li><a href="/wiki/Magnetospheric_eternally_collapsing_object" title="Magnetospheric eternally collapsing object">Magnetospheric eternally collapsing object</a></li> <li><a href="/wiki/Planck_star" title="Planck star">Planck star</a></li> <li><a href="/wiki/Q_star" title="Q star">Q star</a></li> <li><a href="/wiki/Fuzzball_(string_theory)" title="Fuzzball (string theory)">Fuzzball</a></li> <li><a href="/wiki/Geon_(physics)" title="Geon (physics)">Geon</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Analogs</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Optical_black_hole" title="Optical black hole">Optical black hole</a></li> <li><a href="/wiki/Sonic_black_hole" title="Sonic black hole">Sonic black hole</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Lists_of_black_holes" title="Lists of black holes">Lists</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_black_holes" title="List of black holes">Black holes</a></li> <li><a href="/wiki/List_of_most_massive_black_holes" title="List of most massive black holes">Most massive</a></li> <li><a href="/wiki/List_of_nearest_known_black_holes" title="List of nearest known black holes">Nearest</a></li> <li><a href="/wiki/List_of_quasars" title="List of quasars">Quasars</a></li> <li><a href="/wiki/List_of_microquasars" title="List of microquasars">Microquasars</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Outline_of_black_holes" title="Outline of black holes">Outline of black holes</a></li> <li><a href="/wiki/Black_Hole_Initiative" title="Black Hole Initiative">Black Hole Initiative</a></li> <li><a href="/wiki/Black_hole_starship" title="Black hole starship">Black hole starship</a></li> <li><a href="/wiki/Black_holes_in_fiction" title="Black holes in fiction">Black holes in fiction</a></li> <li><a href="/wiki/Big_Bang" title="Big Bang">Big Bang</a></li> <li><a href="/wiki/Big_Bounce" title="Big Bounce">Big Bounce</a></li> <li><a href="/wiki/Compact_star" class="mw-redirect" title="Compact star">Compact star</a></li> <li><a href="/wiki/Exotic_star" title="Exotic star">Exotic star</a> <ul><li><a href="/wiki/Quark_star" title="Quark star">Quark star</a></li> <li><a href="/wiki/Preon_star" class="mw-redirect" title="Preon star">Preon star</a></li></ul></li> <li><a href="/wiki/Gravitational_waves" class="mw-redirect" title="Gravitational waves">Gravitational waves</a></li> <li><a href="/wiki/Gamma-ray_burst_progenitors" title="Gamma-ray burst progenitors">Gamma-ray burst progenitors</a></li> <li><a href="/wiki/Gravity_well" class="mw-redirect" title="Gravity well">Gravity well</a></li> <li><a href="/wiki/Hypercompact_stellar_system" title="Hypercompact stellar system">Hypercompact stellar system</a></li> <li><a href="/wiki/Membrane_paradigm" title="Membrane paradigm">Membrane paradigm</a></li> <li><a href="/wiki/Naked_singularity" title="Naked singularity">Naked singularity</a></li> <li><a href="/wiki/Population_III_star" class="mw-redirect" title="Population III star">Population III star</a></li> <li><a href="/wiki/Supermassive_star" class="mw-redirect" title="Supermassive star">Supermassive star</a></li> <li><a href="/wiki/Quasi-star" title="Quasi-star">Quasi-star</a></li> <li><a href="/wiki/Dark_star_(dark_matter)" title="Dark star (dark matter)">Supermassive dark star</a></li> <li><a href="/wiki/Rossi_X-ray_Timing_Explorer" title="Rossi X-ray Timing Explorer">Rossi X-ray Timing Explorer</a></li> <li><a href="/wiki/Superluminal_motion" title="Superluminal motion">Superluminal motion</a></li> <li><a href="/wiki/Timeline_of_black_hole_physics" title="Timeline of black hole physics">Timeline of black hole physics</a></li> <li><a href="/wiki/White_hole" title="White hole">White hole</a></li> <li><a href="/wiki/Wormhole" title="Wormhole">Wormhole</a></li> <li><a href="/wiki/Tidal_disruption_event" title="Tidal disruption event">Tidal disruption event</a></li> <li><a href="/wiki/Planet_Nine" title="Planet Nine">Planet Nine</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Notable</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cygnus_X-1" title="Cygnus X-1">Cygnus X-1</a></li> <li><a href="/wiki/XTE_J1650-500" class="mw-redirect" title="XTE J1650-500">XTE J1650-500</a></li> <li><a href="/wiki/XTE_J1118%2B480" title="XTE J1118+480">XTE J1118+480</a></li> <li><a href="/wiki/A0620-00" title="A0620-00">A0620-00</a></li> <li><a href="/wiki/Sagittarius_A*" title="Sagittarius A*">Sagittarius A*</a></li> <li><a href="/wiki/Centaurus_A" title="Centaurus A">Centaurus A</a></li> <li><a href="/wiki/Phoenix_Cluster" title="Phoenix Cluster">Phoenix Cluster</a></li> <li><a href="/wiki/PKS_1302-102" title="PKS 1302-102">PKS 1302-102</a></li> <li><a href="/wiki/OJ_287" title="OJ 287">OJ 287</a></li> <li><a href="/wiki/SDSS_J0849%2B1114" title="SDSS J0849+1114">SDSS J0849+1114</a></li> <li><a href="/wiki/TON_618" title="TON 618">TON 618</a></li> <li><a href="/wiki/MS_0735.6%2B7421" title="MS 0735.6+7421">MS 0735.6+7421</a></li> <li><a href="/wiki/NeVe_1" title="NeVe 1">NeVe 1</a></li> <li><a href="/wiki/Hercules_A" title="Hercules A">Hercules A</a></li> <li><a href="/wiki/3C_273" title="3C 273">3C 273</a></li> <li><a href="/wiki/Q0906%2B6930" title="Q0906+6930">Q0906+6930</a></li> <li><a href="/wiki/Markarian_501" title="Markarian 501">Markarian 501</a></li> <li><a href="/wiki/ULAS_J1342%2B0928" title="ULAS J1342+0928">ULAS J1342+0928</a></li> <li><a href="/wiki/PSO_J030947.49%2B271757.31" title="PSO J030947.49+271757.31">PSO J030947.49+271757.31</a></li> <li><a href="/wiki/AT2018hyz" title="AT2018hyz">AT2018hyz</a></li> <li><a href="/wiki/Swift_J1644%2B57" title="Swift J1644+57">Swift J1644+57</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="3" style="text-align:center;"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Black_holes" title="Category:Black holes">Category</a></li> <li><span class="noviewer" typeof="mw:File"><span title="Commons page"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> <a href="https://commons.wikimedia.org/wiki/Category:Black_holes" class="extiw" title="commons:Category:Black holes">Commons</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Roger_Penrose" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Roger_Penrose" title="Template:Roger Penrose"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Roger_Penrose" title="Template talk:Roger Penrose"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Roger_Penrose" title="Special:EditPage/Template:Roger Penrose"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Roger_Penrose" style="font-size:114%;margin:0 4em"><a href="/wiki/Roger_Penrose" title="Roger Penrose">Roger Penrose</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Books</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/The_Emperor%27s_New_Mind" title="The Emperor's New Mind">The Emperor's New Mind</a></i> (1989)</li> <li><i><a href="/wiki/Shadows_of_the_Mind" title="Shadows of the Mind">Shadows of the Mind</a></i> (1994)</li> <li><i><a href="/wiki/The_Road_to_Reality" title="The Road to Reality">The Road to Reality</a></i> (2004)</li> <li><i><a href="/wiki/Cycles_of_Time" title="Cycles of Time">Cycles of Time</a></i> (2010)</li> <li><i><a href="/wiki/Fashion,_Faith,_and_Fantasy_in_the_New_Physics_of_the_Universe" title="Fashion, Faith, and Fantasy in the New Physics of the Universe">Fashion, Faith, and Fantasy in the New Physics of the Universe</a></i> (2016)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Coauthored books</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><span class="wrap"> <i><a href="/wiki/The_Nature_of_Space_and_Time" title="The Nature of Space and Time">The Nature of Space and Time</a></i> (with <a href="/wiki/Stephen_Hawking" title="Stephen Hawking">Stephen Hawking</a>) (1996) </span></li> <li><span class="wrap"> <i><a href="/wiki/The_Large,_the_Small_and_the_Human_Mind" title="The Large, the Small and the Human Mind">The Large, the Small and the Human Mind</a></i> (with <a href="/wiki/Abner_Shimony" title="Abner Shimony">Abner Shimony</a>, <a href="/wiki/Nancy_Cartwright_(philosopher)" title="Nancy Cartwright (philosopher)">Nancy Cartwright</a> and Stephen Hawking) (1997) </span></li> <li><span class="wrap"> <i>White Mars or, The Mind Set Free</i> (with <a href="/wiki/Brian_W._Aldiss" class="mw-redirect" title="Brian W. Aldiss">Brian W. Aldiss</a>) (1999) </span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Twistor_theory" title="Twistor theory">Twistor theory</a></li> <li><a href="/wiki/Spin_network" title="Spin network">Spin network</a></li> <li><a href="/wiki/Abstract_index_notation" title="Abstract index notation">Abstract index notation</a></li> <li><a href="/wiki/Black_hole_bomb" title="Black hole bomb">Black hole bomb</a></li> <li><a href="/wiki/Spacetime" title="Spacetime">Geometry of spacetime</a></li> <li><a class="mw-selflink selflink">Cosmic censorship</a></li> <li><a href="/wiki/Weyl_curvature_hypothesis" title="Weyl curvature hypothesis">Weyl curvature hypothesis</a></li> <li><a href="/wiki/Contributors_to_general_relativity#P" class="mw-redirect" title="Contributors to general relativity">Penrose inequalities</a></li> <li><a href="/wiki/Penrose_interpretation" title="Penrose interpretation">Penrose interpretation of quantum mechanics</a></li> <li><a href="/wiki/Moore%E2%80%93Penrose_inverse" title="Moore–Penrose inverse">Moore–Penrose inverse</a></li> <li><a href="/wiki/Newman%E2%80%93Penrose_formalism" title="Newman–Penrose formalism">Newman–Penrose formalism</a></li> <li><a href="/wiki/Penrose_diagram" title="Penrose diagram">Penrose diagram</a></li> <li><a href="/wiki/Penrose%E2%80%93Hawking_singularity_theorems" title="Penrose–Hawking singularity theorems">Penrose–Hawking singularity theorems</a></li> <li><a href="/wiki/Riemannian_Penrose_inequality" title="Riemannian Penrose inequality">Riemannian Penrose inequality</a></li> <li><a href="/wiki/Penrose_process" title="Penrose process">Penrose process</a></li> <li><a href="/wiki/Penrose_tiling" title="Penrose tiling">Penrose tiling</a></li> <li><a href="/wiki/Penrose_triangle" title="Penrose triangle">Penrose triangle</a></li> <li><a href="/wiki/Penrose_stairs" title="Penrose stairs">Penrose stairs</a></li> <li><a href="/wiki/Penrose_graphical_notation" title="Penrose graphical notation">Penrose graphical notation</a></li> <li><a href="/wiki/Penrose_transform" title="Penrose transform">Penrose transform</a></li> <li><a href="/wiki/Terrell_rotation" title="Terrell rotation">Penrose–Terrell effect</a></li> <li><a href="/wiki/Orchestrated_objective_reduction" title="Orchestrated objective reduction">Orchestrated objective reduction</a>/<a href="/wiki/Penrose%E2%80%93Lucas_argument" title="Penrose–Lucas argument">Penrose–Lucas argument</a></li> <li><a href="/wiki/Free-orbit_experiment_with_laser_interferometry_X-rays" title="Free-orbit experiment with laser interferometry X-rays">FELIX experiment</a></li> <li><a href="/wiki/Trapped_surface" title="Trapped surface">Trapped surface</a></li> <li><a href="/wiki/Andromeda_paradox" class="mw-redirect" title="Andromeda paradox">Andromeda paradox</a></li> <li><a href="/wiki/Conformal_cyclic_cosmology" title="Conformal cyclic cosmology">Conformal cyclic cosmology</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Lionel_Penrose" title="Lionel Penrose">Lionel Penrose</a> (father)</li> <li><a href="/wiki/Oliver_Penrose" title="Oliver Penrose">Oliver Penrose</a> (brother)</li> <li><a href="/wiki/Jonathan_Penrose" title="Jonathan Penrose">Jonathan Penrose</a> (brother)</li> <li><a href="/wiki/Shirley_Hodgson" title="Shirley Hodgson">Shirley Hodgson</a> (sister)</li> <li><a href="/wiki/John_Beresford_Leathes" title="John Beresford Leathes">John Beresford Leathes</a> (grandfather)</li> <li><a href="/wiki/Illumination_problem" title="Illumination problem">Illumination problem</a></li> <li><a href="/wiki/Quantum_mind" title="Quantum mind">Quantum mind</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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