Cosmic Censorship: Does it Hold?

[john baez]

TL;DR

A quick intro to cosmic censorship

I seem to be getting pulled into the project of updating this FAQ:

• https://math.ucr.edu/home/baez/physics/General/open_questions_new.html.

The more I look at it, the bigger the job gets. I started out rewriting the section on neutrinos, and now I'm doing the part on cosmic censorship. There are even bigger jobs to come. But it's fun as long as I don't try to do it all in one go!

Here's the new section on cosmic censorship. If you have any questions or have other good resources to suggest, let me know.

Does Cosmic Censorship hold? Roughly, is general relativity a deterministic theory - and when an object collapses under its own gravity, are the singularities that might develop guaranteed to be hidden behind an event horizon?

Proving a version of Cosmic Censorship is a matter of mathematical physics rather than physics per se, but doing so would increase our understanding of general relativity. There are actually at least two versions: Penrose formulated the "Strong Cosmic Censorship Conjecture" in 1986 and the "Weak Cosmic Censorship Hypothesis" in 1988. Very roughly, strong cosmic censorship asserts that under reasonable conditions general relativity is a deterministic theory, while weak cosmic censorship asserts that that any singularity produced by gravitational collapse is hidden behind an event horizon. Despite their names, strong cosmic censorship does not imply weak cosmic censorship.

In 1991, Preskill and Thorne made a bet against Hawking in which they claimed that weak cosmic censorship was false. Hawking conceded this bet in 1997 when a counterexample was found by Matthew Choptuik. This features finely-tuned infalling matter poised right on the brink of forming a black hole. It almost creates a region from which light cannot escape - but not quite. Instead, it creates a naked singularity!

Given the delicate nature of this construction, Hawking did not give up. Instead he made a new bet, which says that weak cosmic censorship holds "generically - that is, except for very unusual conditions that require infinitely careful fine-tuning to set up. For an overview see:

• Robert Wald, Gravitational Collapse and Cosmic Censorship.

In 1999, Demetrios Christodoulou proved that for spherically symmetric solutions of Einstein's equation coupled to a massless scalar field, weak cosmic censorship holds generically. For a review of this and also Choptuik's work, see:

• Carsten Gundlach, Critical Phenomena in Gravitational Collapse.

While spherical symmetry is a very restrictive assumption, this result is a good example of how, with plenty of work, we can make progress in rigorously settling the questions raised by general relativity.

In 2017, evidence was found to doubt the strong cosmic censorship conjecture, but again a modified version was proposed to save it:

• Kevin Hartnett, Mathematicians Disprove Conjecture Made to Save Black Holes.

 

[haushofer]

Your first link to the Wald-paper links to the Christodoulou-paper instead; it should be

https://arxiv.org/abs/gr-qc/9710068

;)

Studying cosmic censorship seems like a good way to start the new year!

 

[john baez]

Your first link to the Wald-paper links to the Christodoulou-paper instead; it should be

https://arxiv.org/abs/gr-qc/9710068

Whoops, I'll fix that in the FAQ.

The paper by Christodoulou is too technical for the FAQ, btw.

Happy New Year!