Cosmic censorship hypothesis

In general relativity, the cosmic censorship hypothesis is a conjecture about the nature of singularities in spacetime.

The fundamental concern is that, since the physical behavior of singularities is unknown, if singularities can be seen from the rest of spacetime, physics may be unpredictable. We cannot avoid the issue, since by the Penrose-Hawking singularity theorems, singularities are inevitable in physically reasonable situations. The cosmic censorship hypothesis proposes that singularities are always hidden within event horizons, and therefore cannot be seen from the rest of spacetime. Singularities which are not so hidden are called naked.

The hypothesis was first formulated by Roger Penrose in 1969. 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 and that can be proved to be true or false (and that is sufficiently general to be interesting).

There are a number of difficulties in formalizing the hypothesis:

• there are technical difficulties with properly formalizing the notion of a singularity.
• it is not difficult to construct spacetimes which have naked singularities, but which are not "physically reasonable". A formal statement needs some set of hypotheses which exclude these situations.
• It could happen that an observor inside the event horizon could see the singularity. The version of the conjecture which excludes this case is the strong cosmic censorship hypothesis.
• Caustics may occur in simple models of gravitational collapse, 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.
• 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 hypothesis.

In 1991 Stephen Hawking bet Kip Thorne and John Preskill that the hypothesis was true. He lost the bet due to the discovery of the special situations just mentioned. He later said he should have been more careful about the wording of the bet.

References

• Earman, John: Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausalities in Relativistic Spacetimes (1995), see especially chapter 2 (ISBN 0-19-509591-X)
• Penrose, Roger: "The Question of Cosmic Censorship", Chapter 5 in Black Holes and Relativistic Stars, Robert Wald (editor), (1994) (ISBN 0-226-87034-0)
• Penrose, Roger: "Singularities and time-asymmetry", Chapter 12 in General Relativity: An Einsten Centenary Survey (Hawking and Israel, editors), (1979), see especially section 12.3.2, pp. 617-629 (ISBN 0-521-22285-0)
• Shapiro, S. L., and Teukolsky, S. A.: "Formation of Naked Singularities: The Violation of Cosmic Censorship", Physical Review Letters 66, 994-997 (1991)
• Wald, Robert, General Relativity, 299-308 (1984) (ISBN 0-226-87033-2)