The Schwarzschild Geometry: Part 4 - Comments

[PeterDonis]

I still feel that an incomplete spacetime is physically unhealthy in some way, as it means that there are some observers who can reach a region of "Here be dragons" in finite proper time.

I think that is the way most physicists look at it.

Perhaps that is simply the best that GR can say about such spacetimes, and an obvious indication that the theory cannot be fundamental

Yes. The problem is that we don't (yet) have a more fundamental theory that covers the regime that GR does not.

 

[martinbn]

But I still feel that an incomplete spacetime is physically unhealthy in some way, as it means that there are some observers who can reach a region of "Here be dragons" in finite proper time. Perhaps that is simply the best that GR can say about such spacetimes, and an obvious indication that the theory cannot be fundamental (since it cannot answer physically reasonable questions about what happens to some observers).

My personal view is that incompleteness as in the Schwartzschild solution is OK. The observer is torn apart by infinite curvature and ceases to exists, but everyone is accounted for. Incompleteness as in the Kerr solution, where the observer reaches the Cauchy horizon in finite proper time and there is no unique extension beyond it, is not OK. The theory loses its predictability. But this is where the strong cosmic censorship conjecture comes in. If true, these situations are non generic and therefore the theory is still as good as ever.

 

[PAllen]

My personal view is that incompleteness as in the Schwartzschild solution is OK. The observer is torn apart by infinite curvature and ceases to exists, but everyone is accounted for. Incompleteness as in the Kerr solution, where the observer reaches the Cauchy horizon in finite proper time and there is no unique extension beyond it, is not OK. The theory loses its predictability. But this is where the strong cosmic censorship conjecture comes in. If true, these situations are non generic and therefore the theory is still as good as ever.

The cosmic censorship I'm familiar with only requires the BH be surrounded by a horizon. It doesn't say anything about the a-causality of the manifold inside the inner horizon. Does the strong version go further and say something like no singularity in the past light cone of any observer? This would require rejection of the inner horizon region due to CTCs. It also would reject the full Kruskal geometry.

[Ok, I looked this up, and I was only familiar with the weak censorship hypothesis. The strong would, indeed, say the interior of the Kerr Couchy horizon is a violation, and must be non-generic, if true. Does anyone know of much evidence or argument about the strong conjecture? Most discussion, e.g. Hawking's bets, revolve around the weak form, which already had to be modified to avoid a disproof of its simpler form.]

 

[Haelfix]

Yes. The problem is that we don't (yet) have a more fundamental theory that covers the regime that GR does not.

The way I understand cosmic censorship is that it is a research program that specifically tries not to appeal to a different theory. So it wouldn't merely be a statement that say quantum mechanics regulates the problems with the singularity, rather something about the mathematics behind the singularity structure in classical GR allows you to do that. So for instance the original definition of strong cosmic censorship was that you could only have spacelike singularities in physically reasonable theories with gravitational collapse (modulo some details that prevented simple counterexamples from being formulated)

I share Ben Niehoffs view that simply excising the singularity in the standard way done in textbooks counts as a rather *hard* regularization scheme, which perhaps misses some of the details that might help prove or disprove the conjecture. Perusing some of the work that's been done on the subject one can see that there have been multiple approaches and redefinitions and that there is no consensus on which direction to even take. So it stands more on simple physical arguments like the one's already given in the thread, and does not appear to have the correct mathematical formulation yet.