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This question is largely based on the last post by reddit user RobotRollCall who gave some fantastic explanations of phenomena in relativity on a layman's level. About a year ago, she said:

The short answer is that the "singularity" of which you speak is a mathematical artifact that only arises under certain conditions, and cannot meaningfully be said to exist. A black hole consists of an event horizon and nothing else.

Everything I've read up until now, however, contradicts that. As far as I understand, the Hawking-Penrose singularity theorems give nice (and fairly lax/physical) restrictions on a spacetime under which black holes must form true singularities. Is this the case, or is there something I haven't read up on so far which suggests that the singularity theorems do not apply in general? I'm aware that they're really for classical GR, but does quantum physics invalidate them?

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There are two subtly different questions here: (1) "Can non-quantum GR self-consistently contain singularities in a meaningful way?" (to which a reply might be, "yes, consider the Big Bang...") and (2) "Are all singularities (just black holes? coordinate as well as true singularities? there is ambiguity already) expected to be masked in some way by QM?" –  Chris White Jun 25 '13 at 1:00
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@ChrisWhite: Re (1), it doesn't make sense to ask whether GR is self-consistent (it's just a differential equation), but it does make sense to ask whether it gives uniqueness and existence for Cauchy problems. This boils down to global hyperbolicity (Hawking and Ellis, p. 206). Global hyperbolicity fails if cosmic censorship fails, but it doesn't fail simply because singularities exist. –  Ben Crowell Jun 25 '13 at 3:02

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The most common interpretation is that these theorems prove that at the Big Bang and in the astrophysical collapse of a black hole, we really do get densities as extreme as the Planck density.

I don't think any professional physicists believe that the process of forming a singularity proceeds as described in the singularity theorems to densities beyond the Planck density. It's widely accepted that under these conditions, quantum effects are strong and we can't trust classical GR.

There is a little more wiggle room for the idea that the density might stop short of the Planck density. There is a field of semiclassical gravity (e.g., Visser 2009), and if you take their techniques seriously, it's possible that in the astrophysical collapse of a black hole, classical GR fails far below the Planck scale. I think very few relativists or people working on quantum gravity would be willing to bet a six-pack that this is right, because there are serious questions as to the validity of the techniques used in semiclassical gravity. (They have to do some pretty funky renormalizations, and there is no contact with experiment.)

The short answer is that the "singularity" of which you speak is a mathematical artifact that only arises under certain conditions, and cannot meaningfully be said to exist. A black hole consists of an event horizon and nothing else.

The first sentence is reasonably accurate, if you keep in mind that there is indeed something very, very dense inside a black hole, and the early universe was indeed very, very dense. The second sentence sounds silly, although maybe it would be less absurd if put in context. Mass-energy is locally conserved in GR, so the mass of the collapsing body has to be in there somewhere.

Visser, "Small, dark, and heavy: But is it a black hole?," http://arxiv.org/abs/0902.0346

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So might the original quote be more accurate if it were to say that we don't really have an fully accepted model that tells us what's going on with inside black holes, but it looks like it's probably not a singularity like you'd find in classical GR? –  JohnnyMo1 Jun 25 '13 at 2:47
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@JohnnyMo1: IMO that's too weak. We have a pretty clear idea that there's some object at the center that is very, very small and very, very dense, and it has the same mass as the matter that initially collapsed. If you take a solar mass and divide by the Planck density, you get a volume of about $10^{-67}$ cubic meters. –  Ben Crowell Jun 25 '13 at 2:53
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@BenCrowell : For an outside fixed observer, there is nothing beyond the horizon. And for a free falling observer, the "end" is the singularity (or near the sigularity). So it depends on which kind of observer we are talking. The world is not the same seen by different observers. –  Trimok Jun 25 '13 at 9:52

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