phinds said:
He REPEATEDLY said that a black hole is a singularity, continuing to do so after having been told 6 or 7 times that it is not. That seems very troll-like to me, as I pointed out in the thread.
Yes. I definitely noticed that.
In the OP, he stated, "It is a singularity, where a star collapses into a single point in space."
He also said, "A point cannot accrue anything, otherwise it wouldn't be a point any longer, hence couldn't be a black hole."
His reasoning is that if everything keeps falling until it reaches the same "place", then the black hole is in that "place".
On the very first response,
@PeroK was explicit and spot on with his explanation. Unfortunately, "extended spacetime geometry" and "breakdown of the mathematical model" totally overshoot the target.
This is evident in his response: "I know it has an event horizon. But a singularity is a singularity. A single point in 'space time' according to math or 'reality'. [How are they connected?]" (I rephrased his poorly stated question).
@PeroK responded "... It's not a point in space." Simple enough, but you haven't disturbed his image of material falling to a single point-like final destination.
@Bandersnatch responded (in part): "Does it make physical sense for all the mass to be compressed to zero size? - maybe? possibly not? But you can still use your physics toolkit to try and describe in a self-consistent manner what the interior would look like, in terms of fields and geometry and causal interactions, with all the mass in the singularity and otherwise empty. Once you assume that there can be a mass in the form of a singularity, then it shouldn't matter to you whether that mass is X or 2X or X+1 or any other amount."
I think
@Bandersnatch 's response came close enough to the target that the OP focused more specifically on his issue: "One infinite in space should be just as infinite as the other."
This reveals a few misconceptions. One is the nature of singularities. But
@Bandersnatch addressed another one: "It isn't. A black hole is a mass surrounded by the event horizon. That may or may not have a singularity in it."
The OP responds: "An event horizon is when nothing can escape the gravitational pull. So what does that except a singularity? Still doesn't answer my question.".
At this point, team PhysicForum pretty much gave up. Well, not really
@russ_watters gave it a shot.
I would've suggest this - though after reading through the posts, I am convincing myself that it could be futile:
Any suitably dense mass (such as a collapsing star) will create an event horizon. It doesn't have to be a singularity.
When we follow the rules of General Relativity (GR), whatever that dense mass started out as would inevitably continue to a singularity. But chances are, that's not exactly what happens because that GR model completely ignores quantum mechanics (QM). It would be really great if Physicists could describe the whole thing, but that QM part hasn't been nailed down yet. They're working on it.
More to your point (no pun intended), any physical singularity still has to obey conservation of mass. So, combining two physical points will result in a physical point with the sum of the masses (whatever a "physical point" is).
And from a Math stand point, performing a circular integral around two singularities will result is the sum of the integrals around each one - even if they lie at the same point. So, singularities (whether physical of Mathematical) need not be as featureless as you presume.
One more thing: It is not the singularity's mass that is infinite. It is presumably the mass density. Your attempt to then calculate the mass by multiplying the volume (presumably zero) with the density (infinite), just doesn't work. The precise reason for this is a bit technical, but it's because "infinity" is a cardinality, not a number.