[Bill S (OP)]

It is not unusual to meet the idea that GR says that all matter/energy in a black hole is crushed into a singularity with zero volume, but is that right?

Would it be more accurate to say that GR predicts the black hole; but trying to identify a spacetime object at its centre would be extrapolating beyond the limits of GR?. 

[evan_au]

I have seen graphical representations of light cones outside and inside a black hole.
- Inside the black hole, your entire future ends at the singularity, no matter how you accelerate.

I didn't study General Releativity at university, but I found this video instructive (and it's the first time I've seen a Penrose diagram in action...).
See (15 minutes):

[Bill S (OP)]

At last found 15 mins to watch the video.  I’ll need to watch it again, but one thing to which I must give some thought is the assertion that “the singularity becomes a future time, not a central place.”  Any relatively simple observations would be appreciated.

[yor_on]

What I see as true is that it is a singularity. Your wristwatch should function just as good inside as well as outside a event horizon though, and the idea of 'space' surpassing the speed of light inside a event horizon makes little sense to me. I can see where it comes from, it's mathematics.  The accelerating expanding vacuum will depending on choice act as if it was 'moving' stars faster than light, but there is no movement involved locally measured from any side of this observation. Talking about a 'speed' for a patch of a vacuum is meaningless unless you have consistent reference points that you can 'measure' it by, and I don't expect you to have that inside a event horizon, as well as you locally defined will find no speed (gravitational acceleration) acting on you when 'falling' inside it, ignoring tidal forces..
=

Add to it that G has a speed and it's 'c', so nothing that actually can be touched, measured and/or followed in time will ever 'move' any faster than 'c'.

[Bill S (OP)]

What I see as true is that it is a singularity.

Fine, but does that mean no more than that our mathematical model has broken down, and we don’t really know what we are dealing with?  Of course, we have to have models, and we have to test them.  There is always the possible dichotomy between maths and “reality”, but here, we run into infinities, so even the maths has a probable flaw, somewhere.

Talking about a 'speed' for a patch of a vacuum is meaningless unless you have consistent reference points that you can 'measure' it by, and I don't expect you to have that inside a event horizon,

I wouldn’t expect to find any reference point in a vacuum.  Surely, any point would have to be outside.  I’m a bit unclear about the “mechanics” of containing “a patch of a vacuum” in a physical space.  One might just say that the boundary is an event horizon, and leave it at that, but what would that actually mean?

[Bobolink]

It is not unusual to meet the idea that GR says that all matter/energy in a black hole is crushed into a singularity with zero volume, but is that right?

Would it be more accurate to say that GR predicts the black hole; but trying to identify a spacetime object at its centre would be extrapolating beyond the limits of GR?.

I think this is accurate. 
There is no known force that could overcome gravity and prevent the collapse of the mass of a black hole from becoming a singularity.
Our best current theory of gravity GR, breaks down inside the event horizon resulting in infinites.

So is there a singularity at the center of a black hole?  Maybe.

[jeffreyH]

Where does gravitational attraction come from? Is it particulate in nature? If you have a cavity in the centre of a mass where does the gravity go?

The collapse into a black hole has to start somewhere. It is thought to start at the centre of mass. This being compressed under enormous external pressure. Once the central mass is compressed within its own event horizon it pulls the rest in. The compression is thought to be provided by supernova explosions.

So what compressed first? Is it two individual particles? Then the rest are drawn in or is it a much larger mass. Is there a limit such as the Planck mass? Consider the Schwarzschild radius of a two particle compression. Would this even be possible?

Then consider that a singularly must start at this point. The amount of mass that is first compressed within this radius determines the properties of the singularity.

[Bill S (OP)]

So is there a singularity at the center of a black hole?  Maybe.

Undoubtedly, there’s a mathematical singularity, but this is a bit like Father Christmas.  Appearances notwithstanding, who has seen the real thing?

[Bill S (OP)]

That’s good, thought provoking stuff, Jeffrey, but I think the question:

  Would it be more accurate to say that GR predicts the black hole; but trying to identify a spacetime object at its centre would be extrapolating beyond the limits of GR?

 Is still unanswered.

[jeffreyH]

At the centre of a black hole is something science cannot know for sure. What can be investigated is the minimum amount of mass that is allowed to become a black hole. Can it be an individual particle? If so how on earth is that possible?

If it has to be a multiplicity of particles, then how many? So how the black hole starts its life is critical in pointing you in the right direction to even begin to find an answer to your question.

[Bill S (OP)]

The diversity of responses/approaches in threads like this is a great learning resource, but I was trying to clarify what GR actually said about a BH singularity, rather than trying to fathom its nature.  Of course, one might lead to the other, one step at a time.  It always seems wise to have a secure grasp of the first step.