# Nature of singularities in gravitational collapse

A very terse article giving an overview of the state of cosmic censorship in 99/00. Given it’s brevity I recommend a technical background in the differential topological techniques of GR. I assume that the article was written specifically for the conference proceedings, as this would explain a lot.

Despite the lack of exposition I still think the paper is worthwhile because of section 3. Section 3 gives a succinct summary of the counter examples to cosmic censorship, something that I haven’t seen before (although I haven’t really been looking). In any case this section has plenty of references to follow up which in my opinion makes it valuable.

Section 2 gives an overview of the background results for cosmic censorship. It only, however, presents one weak cosmic censorship theorem of the author’s (Krolak). This is disappointing, but perhaps understandable if my assumption above is correct. At the end of section Krolak jarringly concludes

The final conclusion of this section is that theorems based on methods of Lorentzian geometry do not restrict the occurrence of Cauchy horizons to such a degree that we can accept the cosmic censorship principle.

Krolak gives no reason for this assessment save, perhaps for the counter examples in the next section. I for one would have loved some further exposition here. It is often claimed that that cosmic censorship is alive and well, with evidence both for and against. But these claims seem (to me) to rarely be backed up with an explanation of why the theorems aren’t conclusive and why the counter examples aren’t fatal.

Speaking of which the conjecture in section 3,

If all singularities that arise in space-time are of strong curvature then cosmic censorship holds.

is of great interest. Krolak mentions that the shell focussing spacetimes are a counter example but doesn’t go on to justify the physicality of these examples. Are the singularities stable? Are they of non-zero measure? This complaint is probably not justified when one considers the assumption above, but none-the-less this is something that I want.

I don’t really have the background for the last section on physical measurements of singularities and whether the can determine if the singularity is naked. I do note, however, that the arguments of the section seem to be based on the Kerr black hole and specifically the function $\frac{a}{m}$, where $a$ is the angular momentum and $m$ is the mass. To my theoretical mind this simplification seems to much, but perhaps the uniqueness theorems demonstrate that all black holes are sufficiently close to Kerr for it to not be an issue.

(As a side point that wiki article is in desperate need of love… this talk is much better – and I’m pleased to say that I was there for it!)