If a black hole has an event horizon from which nothing can escape, how do we know that there is a singularity inside? How would we tell the difference between a singularity of zero volume and a ball of tightly compressed matter with a volume greater than zero? If nothing can escape from inside the black hole, how can we tell the difference?
Inside a the event horizon of a black hole, space itself is moving toward the singularity at greater than the speed of light.
Any matter that would maintain any sort of… well what we call matter, no matter how exotic, would need to be able to have the force it exerts between particles act faster than the speed of light.
Do we know for sure that something doesn’t exist? No, but we also have no theories or even hypothesis that something like that does, and in most probability, it doesn’t.
As far as what is at the singularity… well that’s just the thing, the reason it is called a singularity is because that’s where all the laws of physics as we know them break down, so actually predicting what lies at the center of a black hole is hard.
OK, this is complicated, so listen closely; I don’t want to have to type out all of this again.
We don’t.
To elaborate: The best models we have predict that a substance which could make up that residuum cannot exist. But we’re pretty sure that those models have already failed in some way or another a bit before you get to the singularity, anyway. How do the models fail? We don’t know-- If we did, then we’d already have better models, and didn’t I just tell you that these were the best models we have? So absent any actual reason to say otherwise, we say that the singularity has zero volume.
Now, once we do eventually develop those better models, nobody would be particularly surprised to find a small but nonzero ball of something in there. In fact, most physicists would probably bet that we would find such. But just how big would that nonzero size be, for instance? Well, we can make some guesses, but that’s all they are, guesses.
Good question: before 1965 it was an open question as to whether the singularities found in BH solutions were generic features of black holes in general relativity or whether they were features of the highly symmetrical nature of idealized BH solutions. However in 1965 Roger Penrose published a theorem that showed, under certain reasonable conditions, a black hole necessarily meant a spacetime singularity.
Obviously to follow Penrose’s arguments requires some understanding of general relativity, but he basically demonstrated that for a black hole some rays of light must be travelling inwards relative to a set of nested closed surfaces of ever-decreasing size, such that a point is reached where the ray of lights literally have nowhere to go.
However it is worth pointing out that Penrose’s theorem does rely on the aforementioned reasonable conditions holding. Now as for the most part (at least within the context being studied) the conditions are very reasonable, however exotic matter, e.g. matter with a negative mass, doesn’t fulfill those conditions and so if there were such matter at the centre of a black hole the singularity could be avoided. In such a situation we couldn’t tell the difference unless we crossed the event horizon, however there is no evidence that such a matter does or can exist.
Of course Penrose’s singularity theorem is a theorem in general relativity, so may very well not hold in a more advanced theory of gravitation.
What would happen if there was a neutron star and matter was slowly trickling into it? Would it slowly become a bigger and bigger neutron star until it got to a certain mass and then collapse into a black hole at the speed of light? And is that when we would say it has an event horizon? Or is there a time when it’s still a neutron star but it also has an event horizon?
One of the things that’s confusing is that I can understand squishing a ball of matter into a smaller, denser ball. The more you squish it, the smaller and denser it gets. But it seems pretty strange that at some point, squishing a very, very, very dense ball just a bit more causes the matter collapse to a ball of zero volume. It would make more sense to me that squishing the ball that last bit would just make the ball a little smaller and denser, and at that point the event horizon was larger than the ball. The ball has slipped behind the curtain of the event horizon, but it’s still there.
Is there a way to easily explain to someone like me how the matter in a very, very, very dense ball can suddenly all start moving towards the singularity at a certain point? The density of the neutron star means the penultimate atom to land on its surface stays on the surface rather than sinking to the center. But then when the last atom lands and the star collapses, suddenly all the matter can flow to the center unimpeded. What changed in the matter to allow that flow to happen rather than just become denser matter?
The thing about a singularity is that it’s not actually a “thing”; it’s more like a divide-by-zero error in general relativity. The same divide-by-zero error happens in Newtonian gravity, too; if the strength of gravity is inversely proportional to the square of the radius, then the equations simply don’t work if the radius is zero.
However, superstring theory has the idea of the fuzzball; a black hole made of superstrings that has no singularity. Of course, we don’t really know if that’s the way it works, but it’s one possible way.
As a neutron star undergoes its final collapse, the event horizon expands outwards from the center at the speed of light, until at some point the horizon zipping outwards meets the infalling matter zipping inwards, and the transformation into a black hole is complete.
How sure are you about that? It’s not clear to me the nucleation point must be at the center. Isn’t it more likely that there’s a finite volume near the critical density, and then a fluctuation puts a point not at the center above the threshold?
It’s a question of what is stopping the clumping together of all matter. Gravity is king here, but electrons repelling each other is enough to prevent this in our normal experience.
In sufficiently massive stars though, there can be events that put so much stuff so close together, that that breaks down, and that’s where the (actually quite readable) wiki article on degenerate matter comes in:
Basically, the forces/quantum principles that stop stuff clumping together get overcome by gravity, in a sort of cascade effect.
That’s a point I don’t understand. In fully degenerate matter, the collapse is prevented AFAIU because of a quantum law. Something like “if it collapsed anymore, it would violate the Pauli exclusion principle, so it can’t collapse anymore”.
How does gravity overcome a law of physics? I mean yes, the standard reply is “laws of physics fail at singularity” but that’s a bit of a truism. “This happens because it happens”. Why not just say it does not collapse further because the exclusion principle prevents it? It’s behind the event horizon, so there is no way to look and see what exactly happens, so why is singularity a preferred explanation?
What happens to time within the event horizon, and at this singularity? … if we say “a singularity has zero volume”, do you mean volume in a three dimensional sense, or is there a four dimensional equivalency …
Maybe we could Chronos type in his comment above again …
The truth is there’s no Universal clock or non-arbitrary way of imposing one, so it is arbitrary to assign a universal sense of ‘when’ an event happens.
However what can be said in spherically symmetric collapse is that, at the event of any layer of the star crossing the event horizon, the event of any more inner layer of the star crossing the event horizon will be in the causal past. So in the sense that we could construct a coordinate system that respects causal structure, and covers when all the layers of the stars are at event horizon, the event horizon must go from the centre and spread outwards.
NB though I’ve assumed that, due to spherical symmetry, all the points on a layer of the star must cross the event horizon at the same time.
You misunderstand: it overcomes a pressure due to the Pauli exclusion principle, that is certainly not the same as violating the PEP.
Didn’t Stephen Hawking posit imaginary time as a way to eliminate singularities from the math?
Ok. What force is responsible for the pressure that is due to the PEP?
I am very far from being proficient in quantum physics, but my understanding was that the degeneracy pressure was wholly due to the non-violation of the PEP and not to any particular force. Which, if true, is a pretty amazing thing… basically a pure expression of an abstract quantum-physical principle in a macro universe.
But then maybe I am completely misinterpreting what I read.
The PEP creates a degeneracy pressure in a fermion gas, but that pressure only goes to infinity as the density goes to infinity. As at higher densities degeneracy pressure will dominate, it is always possible to compress a fermion gas, no matter how dense it is.
Gravity in general relativity effectively requires an infinite pressure to resist for a spherically symmetrically distributed gas of total mass M when the density goes to k/M[sup]2[/sup] (where k is some constant with appropriate units). At the crudest level, k will give a value such that the gas will be at its Schwarzschild radius, though it is not that difficult to show k must be a bit larger than this, regardless of the properties of the gas.
As the degeneracy pressure only goes to infinity as density goes to infinity, this means that a fermion gas must become unstable and collapse under its own gravity when its density is at some value less than k/M[sup]2[/sup]
There’s no global measure of time, but beyond the event horizon nothing special happens locally, indeed if the black hole is big enough such that the spacetime curvature only gets extreme some way past the horizon you would not even notice that you had crossed the horizon.
The singularity is where spacetime ends and as such is not part of spacetime, so a literal reading of the model would mean that time suddenly ends when you hit the singularity. There is a 4D equivalent to volume, but the singularity has no volume in any meaningful sense.
I was working in a spherically-symmetric model of stellar collapse, for no reason other than that it’s simplest. Modern simulations have shown that the assumption of spherical symmetry isn’t actually a very good one, and so the “center” of the forming event horizon probably won’t actually be at the center of the star. But it’ll still expand outwards from some point (or points).
And degeneracy pressure is always due to some force or another. Yes, yes, it’s due to the Pauli exclusion principle, but the PEP doesn’t say that two particles can’t be in the “same place”, it says that they can’t be in the same state. Location is part of state, of course, but how “big” each state is depends on the forces involved. So if, for instance, the dominant force is the electromagnetic one (as it is in a white dwarf), then it’s the electromagnetic force which will determine how the states are arranged, and how close together two electrons can be without both being in the same state, and thus the pressure is due to electromagnetism.
Does that also work for a spherically symmetric shell? Consider a sparse, hollow shell of neutron stars, roughly star-sized, or however small or large it needs to be to avoid collapse. Then another neutron star comes zipping along near the speed of light and intersects the shell. If the rogue neutron star is going fast enough, could it cause a collapse from which it can then escape since it will be outside the event horizon by the time the horizon reaches it?
So a black hole is really a bowl full of tachyon soup?