Black hole question

Buckleymanor

Only at the singularity!

How can GR work if it does not explain the singularity.It's nonesense, you would be better off explaining how an egg boils.
Sorry if this sounds abrupt but to state with conviction that we know how GR works inside the event horizon down to the singularity is just plain wrong.

K^2

Physics isn't meant to be a blueprint to reality. Being part of reality, we have no way of verifying anything to be absolutely correct. Physics is meant to describe what we can observe. General Relativity describes everything we can observe perfectly, as far as we can tell. Certainly, with higher precision than you could hope for with "wishful thinking".

Whether GR describes anything bellow the event horizon properly is an open question. But it's also irrelevant. Absolutely nothing that's happening bellow event horizon could influence anything above. So frankly, as far as Physics goes, it's not relevant. GR works up to event horizon, and that's all it needs to do. Unless we find a flaw in GR's predictions we can test, to the best of our knowledge, it just works. And since absolutely no experiment can be performed on anything bellow event horizon, any failures of GR in that region are of no significance.

Buckleymanor

Tosh! how can you arrive at any conclusion is beyond any known Physics.We don't know if it's of any influence or if it's relivant or not.Why bother looking, might as well say we know as much as we ever will about gravity inside an event horizon so it is of no importance.
We have not actualy performed any experiments just outside of any event-horizons so it's jumping the gun to say the least that non can be performed on anything bellow.
We just don't know at this moment.

K^2

We have a model that works for everything from satellites to neutron stars. And while we have not performed any critical experiments, we have looked at stuff falling into the black hole, and that does seem to agree with theory.

Granted, we cannot absolutely exclude possibility that right next to event horizon all physics as we know it breaks down and something different happens. But we cannot absolutely exclude possibility of existence of pixies and unicorns, either. Yet you aren't going to go around claiming that we just don't know. We do know. At this point, possibility of GR being completely wrong is in realm of fantasy and fairy tales.

It could not be entirely precise. There might be corrections that would alter the location of event horizon, for example. Or some additional contributions to gravity to explain motion of distant galaxies. But it's not going to be something that invalidates GR. Merely corrects it. Just like GR did not invalidate Newtonian Gravity in general. We could predict the motion of distant moons before GR, and we could after.

phinds

Uh ... you don't seem to quite get the concept of event horizon and why we can't perform experiments below it and never will be able to, by definition.

PeterDonis

That's not quite correct. Experiments can be performed below the horizon, but information about their results can never be sent back outside the horizon.

phinds

Yeah, you are right of course and I thought about adding exactly that in my post, but it seemed irrelevant to the point of the incorrect statement I was addressing.

Buckleymanor

Well if we can't that by definition would be an experiment to verify if it were a black hole.

Warp

According to General Relativity a singularity inside a black hole has zero volume and finite mass (which effectively makes its density infinite.) According to it, it's impossible for it to have non-zero volume because no particle inside the event horizon can avoid moving towards the singularity. (Even going forward in time makes the particle go towards the singularity. No amount of energy can stop it from moving towards it. In fact, and ironically, applying energy would only accelerate it towards the singularity.)

The "size" of a black hole is determined by its mass. The mass doesn't change even if it's compressed into a singularity. (And "size" refers to the radius of the event horizon, which in itself isn't anything physical. It's simply a zone of curved spacetime with some specific characteristics. The most prominent one is that whatever goes in can never come out.)

A singularity doesn't need to be a point. For a non-rotating, non-charged black hole it's a point, but in practice no black hole is like that because stars always rotate. (So-called primordial black holes, if they exist, might in theory be an exception to this.) In a rotating black hole the singularity will actually be a ring of zero volume (a so-called ring singularity.)

If we consider GR on its own, there's no reason to believe that singularities don't exist. That's because everything that we can measure seems to conform to GR quite well, and so far there's little reason to think otherwise even if we extrapolate to the extremes (such as matter collapsing into its own schwarzschild radius.)

Quantum physics might have an effect on this, and might cause true singularities to not exist, but so far no unified theory has been found to describe this.

pervect

Most people think that the laws of quantum mechanics will mean that a black hole has a finite size. However, we don't know what that finite size is - is it the size of a marble? An atom? Smaller? Nobody knows for sure. We would need a quantum theory of gravity to answer that question, and we don't have one. The theory we do have is GR, but GR cannot answer your question.

GR can tell us other things about black holes though - the size of the event horizon. Gr gives us the schwarzschild radius, and 4*pi*r_s^2 (where r_s is the schwarzschild radius0 is the area of the event horizon.

leroyjenkens

So zero volume isn't a meaningful answer? So why is it being reported as the truth?

Warp

It's not "reported as the truth". It's the prediction made by General Relativity.

There are good reasons why that prediction isn't simply discarded as silly. General Relativity has passed test after test with a brilliant score. Almost everything that we can measure seems to conform quite well to its predictions. There are very few scientific theories that have been so well tested and corroborated. It's the reason why when it was discovered that galaxies rotate in an unexpected manner GR was not just thrown out, but instead we are puzzling about what exactly is it that makes them rotate like that. Likewise for the accelerating expansion of the universe.

The same equations predict that particles inside the event horizon of a black hole cannot stay out of the central singularity. A physical impossibility.

The dilemma is, however, that GR does not work well when sizes get very small. GR cannot describe things at quantum levels very well (for instance, GR has no explanation whatsoever for the double slit experiment; reality gets extremely weird at those scales and GR just doesn't work there.)

And that's the problem. You can't get smaller than a singularity, so ostensibly quantum effects might kick into the equation in one way or another. It's yet unknown if and how.

leroyjenkens

Then why do I see "infinite density" and "zero volume" every time I look up information about black holes? If it's a meaningless answer, like the other guy said, why include it as part of the description of a black hole?

Warp

Because that's what GR predicts.