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href="/nlab/show/super+Poincar%C3%A9+Lie+algebra">super Poincaré Lie algebra</a>, <a class="existingWikiWord" href="/nlab/show/supergravity+Lie+3-algebra">supergravity Lie 3-algebra</a>, <a class="existingWikiWord" href="/nlab/show/supergravity+Lie+6-algebra">supergravity Lie 6-algebra</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/differential+geometry">differential geometry</a></p> </li> <li> <p>(<a class="existingWikiWord" href="/nlab/show/super-Cartan+geometry">super</a>-)<a class="existingWikiWord" href="/nlab/show/Cartan+geometry">Cartan geometry</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/pseudo-Riemannian+manifold">pseudo</a>-<a class="existingWikiWord" href="/nlab/show/Riemannian+manifold">Riemannian manifold</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/spacetime">spacetime</a></p> </li> </ul> </li> </ul> <p><strong>Definition</strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Einstein-Hilbert+action">Einstein-Hilbert action</a>, <a class="existingWikiWord" href="/nlab/show/Einstein%27s+equations">Einstein's equations</a>, <a class="existingWikiWord" href="/nlab/show/general+relativity">general relativity</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/first-order+formulation+of+gravity">first-order formulation of gravity</a>, <a class="existingWikiWord" href="/nlab/show/D%27Auria-Fre+formulation+of+supergravity">D'Auria-Fre formulation of supergravity</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/gravity+as+a+BF-theory">gravity as a BF-theory</a>, <a class="existingWikiWord" href="/nlab/show/Plebanski+formulation+of+gravity">Plebanski formulation of gravity</a>, <a class="existingWikiWord" href="/nlab/show/teleparallel+gravity">teleparallel gravity</a></p> </li> </ul> </li> </ul> <p><strong>Spacetime configurations</strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/spacetime">spacetime</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Minkowski+spacetime">Minkowski spacetime</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/black+hole+spacetime">black hole spacetime</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Schwarzschild+spacetime">Schwarzschild spacetime</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Kerr+spacetime">Kerr spacetime</a></p> </li> </ul> </li> </ul> <p><strong>Properties</strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Kaluza-Klein+mechanism">Kaluza-Klein mechanism</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Bekenstein-Hawking+entropy">Bekenstein-Hawking entropy</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/generalized+second+law+of+thermodynamics">generalized second law of thermodynamics</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/cosmic+censorship+hypothesis">cosmic censorship hypothesis</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/weak+gravity+conjecture">weak gravity conjecture</a></p> </li> </ul> <p><strong>Spacetimes</strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/standard+model+of+cosmology">standard model of cosmology</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Minkowski+spacetime">Minkowski spacetime</a></p> </li> </ul> <div> <table><thead><tr><th><strong><a class="existingWikiWord" href="/nlab/show/black+hole">black hole</a> <a class="existingWikiWord" href="/nlab/show/spacetimes">spacetimes</a></strong></th><th>vanishing <a class="existingWikiWord" href="/nlab/show/angular+momentum">angular momentum</a></th><th><a class="existingWikiWord" href="/nlab/show/positive+number">positive</a> <a class="existingWikiWord" href="/nlab/show/angular+momentum">angular momentum</a></th></tr></thead><tbody><tr><td style="text-align: left;"><strong>vanishing <a class="existingWikiWord" href="/nlab/show/charge">charge</a></strong></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/Schwarzschild+spacetime">Schwarzschild spacetime</a></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/Kerr+spacetime">Kerr spacetime</a></td></tr> <tr><td style="text-align: left;"><strong><a class="existingWikiWord" href="/nlab/show/positive+number">positive</a> <a class="existingWikiWord" href="/nlab/show/charge">charge</a></strong></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/Reissner-Nordstrom+spacetime">Reissner-Nordstrom spacetime</a></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/Kerr-Newman+spacetime">Kerr-Newman spacetime</a></td></tr> </tbody></table> </div> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/asymptotically+flat+spacetime">asymptotically flat spacetime</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/gravitational+wave">gravitational wave</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/anti+de+Sitter+spacetime">anti de Sitter spacetime</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/FRW+spacetime">FRW spacetime</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Taub-NUT+spacetime">Taub-NUT spacetime</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Einstein+manifold">Einstein manifold</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/pp-wave+spacetime">pp-wave spacetime</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/KK-monopole">KK-monopole</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Malament%E2%80%93Hogarth+spacetime">Malament–Hogarth spacetime</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/super+spacetime">super spacetime</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/super+Minkowski+spacetime">super Minkowski spacetime</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/black+brane">black brane</a></p> </li> </ul> <p><strong>Quantum theory</strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+gravity">quantum gravity</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/graviton">graviton</a>, <a class="existingWikiWord" href="/nlab/show/gravitino">gravitino</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/string+theory">string theory</a></p> </li> </ul> </li> </ul> </div></div> </div> </div> <h1 id="contents">Contents</h1> <div class='maruku_toc'> <ul> <li><a href='#idea'>Idea</a></li> <li><a href='#properties'>Properties</a></li> <ul> <li><a href='#relation_to_the_weak_gravity_conjecture'>Relation to the weak gravity conjecture</a></li> </ul> <li><a href='#related_concepts'>Related concepts</a></li> <li><a href='#references'>References</a></li> <ul> <li><a href='#general'>General</a></li> <li><a href='#strong_cosmic_censorship'>Strong cosmic censorship</a></li> <li><a href='#weak_cosmic_censorship'>Weak cosmic censorship</a></li> <li><a href='#more_references'>More references</a></li> </ul> </ul> </div> <h2 id="idea">Idea</h2> <p>The <em>cosmic censorship hypothesis</em> is the name of a pair of <a class="existingWikiWord" href="/nlab/show/conjectures">conjectures</a> (<a href="#Penrose69">Penrose 69</a>) saying that in the <a class="existingWikiWord" href="/nlab/show/theory+%28physics%29">theory</a> of <a class="existingWikiWord" href="/nlab/show/general+relativity">general relativity</a>, under physically reasonable conditions, any <a class="existingWikiWord" href="/nlab/show/singularities">singularities</a> in <a class="existingWikiWord" href="/nlab/show/spacetime">spacetime</a> must lie behind an <a class="existingWikiWord" href="/nlab/show/event+horizon">event horizon</a>.</p> <p>Both the weak and the strong form of the conjecture concern solutions of <a class="existingWikiWord" href="/nlab/show/Einstein%27s+equations">Einstein's equations</a> with physically realistic matter and generic compact or asymptotically flat initial data.</p> <p>The <strong>strong cosmic censorship conjecture</strong>, proposed by Penrose in 1986, states that the maximal Cauchy development of such a solution is locally inextendible as a regular Lorentzian manifold.</p> <p>The <strong>weak cosmic censorship hypothesis</strong>, proposed by him in 1988, asserts that for generic initial data, the maximal <a class="existingWikiWord" href="/nlab/show/Cauchy+surface">Cauchy development</a> of a solution of Einstein’s equations with realistic matter possesses a complete future null infinity.</p> <p>Despite their names, the strong version does not necessarily imply the weak version.</p> <p>Without the ‘genericity’ condition, which needs to be carefully stated, both strong and weak cosmic censorship fail. That is, with carefully fine-tuned <a class="existingWikiWord" href="/nlab/show/initial+value+problem">initial data</a> one can find counterexamples.</p> <h2 id="properties">Properties</h2> <h3 id="relation_to_the_weak_gravity_conjecture">Relation to the weak gravity conjecture</h3> <p>The weak cosmic censorship conjecture has many counterexamples in <a class="existingWikiWord" href="/nlab/show/dimension">dimension</a> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>d</mi><mo>≥</mo><mn>5</mn></mrow><annotation encoding="application/x-tex">d \geq 5</annotation></semantics></math>. <a class="existingWikiWord" href="/nlab/show/Cumrun+Vafa">Cumrun Vafa</a> has argued that the <em><a class="existingWikiWord" href="/nlab/show/weak+gravity+conjecture">weak gravity conjecture</a></em> will save the cosmic censorship conjecture. The weak gravity conjecture says that in consistent theories of <a class="existingWikiWord" href="/nlab/show/quantum+gravity">quantum gravity</a> the gravitational force exerted by any object (e.g. a <a class="existingWikiWord" href="/nlab/show/black+hole">black hole</a>) has to be weaker, in suitable units, than any other force. As discussed in (<a href="#CrisfordSantos17">Crisford-Santos 17</a>) it seems plausible that this constraint would indeed rule out the counterexample constructed there:</p> <blockquote> <p>Subsequent calculations by Santos and Crisford supported Vafa’s hunch; the simulations they’re running now could verify that naked singularities become cloaked in black holes right at the point where gravity becomes the weakest force. (<a href="https://www.quantamagazine.org/where-gravity-is-weak-and-naked-singularities-are-verboten-20170620/">Wolchover, June 20 2017</a>)</p> </blockquote> <p>The <a class="existingWikiWord" href="/nlab/show/weak+gravity+conjecture">weak gravity conjecture</a> was motivated from <a class="existingWikiWord" href="/nlab/show/string+theory">string theory</a>, where there are various plausibility arguments that it holds.</p> <h2 id="related_concepts">Related concepts</h2> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Penrose+singularity+theorem">Penrose singularity theorem</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/weak+gravity+conjecture">weak gravity conjecture</a></p> </li> </ul> <h2 id="references">References</h2> <h3 id="general">General</h3> <p>The original article:</p> <ul> <li id="Penrose69"><a class="existingWikiWord" href="/nlab/show/Roger+Penrose">Roger Penrose</a>, <em>Gravitational collapse: The role of general relativity</em>, Riv. Nuovo Cim. 1 (1969) 252-276, Gen. Rel. Grav. 34 (2002) 1141-1165 (<a href="https://doi.org/10.1023/A:1016578408204">doi:10.1023/A:1016578408204</a>)</li> </ul> <p>Review:</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Roger+Penrose">Roger Penrose</a>, <em>The Question of Cosmic Censorship</em>, Journal of Astrophysics and Astronomy, Vol. 20, p.233, 1999 (<a href="https://doi.org/10.1007/BF02702355">doi:10.1007/BF02702355</a>, <a href="http://adsabs.harvard.edu/full/1999JApA...20..233P">web</a>)</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Klaas+Landsman">Klaas Landsman</a>, <em>Singularities, black holes, and cosmic censorship: A tribute to Roger Penrose</em> (<a href="https://arxiv.org/abs/2101.02687">arXiv:2101.02687</a>)</p> </li> </ul> <p>See also:</p> <ul> <li>Wikipedia, <em><a href="http://en.wikipedia.org/wiki/Cosmic_censorship_hypothesis">Cosmic censorship hypothesis</a></em></li> </ul> <h3 id="strong_cosmic_censorship">Strong cosmic censorship</h3> <p>For strong cosmic censorship, see:</p> <ul> <li>Mihalis Dafermos, <em>Strong cosmic censorship</em> (<a href="http://web.math.princeton.edu/~dafermos/research/structure-of-singularities/strong-cosmic-censorship.html">web</a>)</li> </ul> <p>In 2017 Dafermos and Luk found a counterexample to strong cosmic censorship without the requirement that the initial data be generic:</p> <ul> <li>Mihalis Dafermos and Jonathan Luk, <em>The interior of dynamical vacuum black holes I: The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><msup><mi>C</mi> <mn>0</mn></msup></mrow><annotation encoding="application/x-tex">C^0</annotation></semantics></math>-stability of the Kerr Cauchy horizon</em> (<a href="https://arxiv.org/abs/1710.01722">arXiv:1710.01722</a>)</li> </ul> <p>Discussion in relation to <a class="existingWikiWord" href="/nlab/show/computability+in+physics">computability in physics</a> and <a class="existingWikiWord" href="/nlab/show/Malament%E2%80%93Hogarth+spacetimes">Malament–Hogarth spacetimes</a>:</p> <ul> <li id="Etesi12"><a class="existingWikiWord" href="/nlab/show/Gabor+Etesi">Gabor Etesi</a>, <em>A proof of the Geroch-Horowitz-Penrose formulation of the strong cosmic censor conjecture motivated by computability theory</em> (<a href="http://arxiv.org/abs/1205.4550">arXiv:1205.4550</a>)</li> </ul> <p>In 2020, Hod claimed a “remarkably compact proof” of strong cosmic censorship:</p> <ul> <li>Shahar Hod, <em>A proof of the strong cosmic censorship conjecture</em>, International Journal of Modern Physics D 29, 2042003 (2020) (<a href="https://arxiv.org/abs/2012.01449">arXiv:2012.01449</a>, <a href="https://doi.org/10.1142/S0218271820420031">doi:10.1142/S0218271820420031</a>)</li> </ul> <h3 id="weak_cosmic_censorship">Weak cosmic censorship</h3> <p>Review of weak cosmic censorship:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Robert+Wald">Robert Wald</a>, <em>Gravitational collapse and cosmic censorship</em>, In: Iyer B.R., Bhawal B. (eds) <em>Black Holes, Gravitational Radiation and the Universe</em>, Fundamental Theories of Physics, vol 100. Springer 1999 (<a href="https://arxiv.org/abs/gr-qc/9710068">arXiv:gr-qc/9710068</a>, <a href="https://doi.org/10.1007/978-94-017-0934-7_5">doi:10.1007/978-94-017-0934-7_5</a>)</li> </ul> <p>In 1993 Choptuik found a counterexample to weak cosmic censorship without the requirement that the initial data be generic, by considering a spherically symmetric solution of gravity coupled to a scalar field right on the brink of the formation of a black hole. This and subsequent work is reviewed here:</p> <ul> <li>Carsten Gundlach, <em>Critical phenomena in gravitational collapse</em>, Living Rev. Relativ. 10, 5 (2007) (<a href="https://arxiv.org/abs/gr-qc/0001046">arXiv:gr-qc/0001046</a>, <a href="https://doi.org/10.12942/lrr-2007-5">doi:10.12942/lrr-2007-5</a>)</li> </ul> <p>For a proof of weak cosmic censorship in the spherically symmetric case, see:</p> <ul> <li>Demetrios Christodoulou, The instability of naked singularities in the gravitational collapse of a scalar field, <em>Ann. Math.</em> 149 (1999), 183-217. (<a href="http://arxiv.org/abs/math/9901147">arxiv</a>)</li> </ul> <p>A counterexample in 4-dimensional <a class="existingWikiWord" href="/nlab/show/anti-de+Sitter+spacetime">anti-de Sitter spacetime</a>:</p> <ul> <li id="CrisfordSantos17">Toby Crisford, <a class="existingWikiWord" href="/nlab/show/Jorge+Santos">Jorge Santos</a>, <em>Violating weak cosmic censorship in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><msub><mi>AdS</mi> <mn>4</mn></msub></mrow><annotation encoding="application/x-tex">AdS_4</annotation></semantics></math></em>, Phys. Rev. Lett. 118, 181101 (2017) (<a href="https://arxiv.org/abs/1702.05490">arXiv:1702.05490</a>)</li> </ul> <p>A counterexample in 6-dimensional spacetime:</p> <ul> <li id="AndradeFiguerasSperhake20">Tomas Andrade, Pau Figueras, Ulrich Sperhake, <em>Violations of Weak Cosmic Censorship in black hole collisions</em> (<a href="https://arxiv.org/abs/2011.03049">arXiv:2011.03049</a>)</li> </ul> <h3 id="more_references">More references</h3> <p>For <a class="existingWikiWord" href="/nlab/show/BTZ+black+holes">BTZ black holes</a>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Roberto+Emparan">Roberto Emparan</a>, Marija Tomašević, <em>Strong cosmic censorship in the BTZ black hole</em>, JHEP 06 (2020) 038 (<a href="https://arxiv.org/abs/2002.02083">arXiv:2002.02083</a>)</li> </ul> <p>Relation to the <a class="existingWikiWord" href="/nlab/show/weak+gravity+conjecture">weak gravity conjecture</a>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Gary+Horowitz">Gary Horowitz</a>, <a class="existingWikiWord" href="/nlab/show/Jorge+Santos">Jorge Santos</a>, <em>Further evidence for the weak gravity - cosmic censorship connection</em> (<a href="https://arxiv.org/abs/1901.11096">arXiv:1901.11096</a>)</li> </ul> <p>Relation to <a class="existingWikiWord" href="/nlab/show/higher+curvature+corrections">higher curvature corrections</a>:</p> <ul> <li>Akash K Mishra, Sumanta Chakraborty, <em>Strong Cosmic Censorship in higher curvature gravity</em>, Phys. Rev. D 101, 064041 (2020) (<a href="https://arxiv.org/abs/1911.09855">arXiv:1911.09855</a>)</li> </ul> </body></html> </div> <div class="revisedby"> <p> Last revised on July 4, 2024 at 16:54:40. 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