nLab cosmic censorship hypothesis

Idea

The cosmic censorship hypothesis is the name of a pair of conjectures (Penrose 69) saying that in the theory of general relativity, under physically reasonable conditions, any singularities in spacetime must lie behind an event horizon.

Both the weak and the strong form of the conjecture concern solutions of Einstein's equations with physically realistic matter and generic compact or asymptotically flat initial data.

The strong cosmic censorship conjecture, proposed by Penrose in 1986, states that the maximal Cauchy development of such a solution is locally inextendible as a regular Lorentzian manifold.

The weak cosmic censorship hypothesis, proposed by him in 1988, asserts that for generic initial data, the maximal Cauchy development of a solution of Einstein’s equations with realistic matter possesses a complete future null infinity.

Despite their names, the strong version does not necessarily imply the weak version.

Without the ‘genericity’ condition, which needs to be carefully stated, both strong and weak cosmic censorship fail. That is, with carefully fine-tuned initial data one can find counterexamples.

Properties

Relation to the weak gravity conjecture

The weak cosmic censorship conjecture has many counterexamples in dimension $d \geq 5$. Cumrun Vafa has argued that the weak gravity conjecture will save the cosmic censorship conjecture. The weak gravity conjecture says that in consistent theories of quantum gravity the gravitational force exerted by any object (e.g. a black hole) has to be weaker, in suitable units, than any other force. As discussed in (Crisford-Santos 17) it seems plausible that this constraint would indeed rule out the counterexample constructed there:

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. (Wolchover, June 20 2017)

The weak gravity conjecture was motivated from string theory, where there are various plausibility arguments that it holds.

Related concepts

• Penrose singularity theorem

• weak gravity conjecture

References

General

The original article:

• Roger Penrose, Gravitational collapse: The role of general relativity, Riv. Nuovo Cim. 1 (1969) 252-276, Gen. Rel. Grav. 34 (2002) 1141-1165 (doi:10.1023/A:1016578408204)

Review:

• Roger Penrose, The Question of Cosmic Censorship, Journal of Astrophysics and Astronomy, Vol. 20, p.233, 1999 (doi:10.1007/BF02702355, web)

• Klaas Landsman, Singularities, black holes, and cosmic censorship: A tribute to Roger Penrose (arXiv:2101.02687)

See also:

• Wikipedia, Cosmic censorship hypothesis

Strong cosmic censorship

For strong cosmic censorship, see:

• Mihalis Dafermos, Strong cosmic censorship (web)

In 2017 Dafermos and Luk found a counterexample to strong cosmic censorship without the requirement that the initial data be generic:

• Mihalis Dafermos and Jonathan Luk, The interior of dynamical vacuum black holes I: The $C^0$-stability of the Kerr Cauchy horizon (arXiv:1710.01722)

Discussion in relation to computability in physics and Malament–Hogarth spacetimes:

• Gabor Etesi, A proof of the Geroch-Horowitz-Penrose formulation of the strong cosmic censor conjecture motivated by computability theory (arXiv:1205.4550)

In 2020, Hod claimed a “remarkably compact proof” of strong cosmic censorship:

• Shahar Hod, A proof of the strong cosmic censorship conjecture, International Journal of Modern Physics D 29, 2042003 (2020) (arXiv:2012.01449, doi:10.1142/S0218271820420031)

Weak cosmic censorship

Review of weak cosmic censorship:

• Robert Wald, Gravitational collapse and cosmic censorship, In: Iyer B.R., Bhawal B. (eds) Black Holes, Gravitational Radiation and the Universe, Fundamental Theories of Physics, vol 100. Springer 1999 (arXiv:gr-qc/9710068, doi:10.1007/978-94-017-0934-7_5)

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:

• Carsten Gundlach, Critical phenomena in gravitational collapse, Living Rev. Relativ. 10, 5 (2007) (arXiv:gr-qc/0001046, doi:10.12942/lrr-2007-5)

For a proof of weak cosmic censorship in the spherically symmetric case, see:

• Demetrios Christodoulou, The instability of naked singularities in the gravitational collapse of a scalar field, Ann. Math. 149 (1999), 183-217. (arxiv)

A counterexample in 4-dimensional anti-de Sitter spacetime:

• Toby Crisford, Jorge Santos, Violating weak cosmic censorship in $AdS_4$, Phys. Rev. Lett. 118, 181101 (2017) (arXiv:1702.05490)

A counterexample in 6-dimensional spacetime:

• Tomas Andrade, Pau Figueras, Ulrich Sperhake, Violations of Weak Cosmic Censorship in black hole collisions (arXiv:2011.03049)

More references

For BTZ black holes:

• Roberto Emparan, Marija Tomašević, Strong cosmic censorship in the BTZ black hole, JHEP 06 (2020) 038 (arXiv:2002.02083)

Relation to the weak gravity conjecture:

• Gary Horowitz, Jorge Santos, Further evidence for the weak gravity - cosmic censorship connection (arXiv:1901.11096)

Relation to higher curvature corrections:

• Akash K Mishra, Sumanta Chakraborty, Strong Cosmic Censorship in higher curvature gravity, Phys. Rev. D 101, 064041 (2020) (arXiv:1911.09855)