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I've often seen black holes referred to as having a "singularity", which is described as a point of "infinite density", presumably due to the mass of the black hole occupying a point with zero volume (rather than having infinite mass in a finite volume).

Is there any evidence that this singularity is actually infinitely small, as opposed to just "extremely small"? For example, if it's the size of a quark (i'm just choosing a quark as an example of a "extremely small thing") then it's not infinitely small, it's just extremely small, and the density will just be extremely high rather than infinitely high.

I understand that due to the event horizon, we don't really know what's going on in there. But, since we know that the event horizon has a finite volume, why not assume that the black hole itself (or "the thing at the middle" - i'm not sure if the term "black hole" includes the event horizon or not) has a finite volume too?

Is the "infinite density" thing actually just a common misperception by writers?

EDIT - i just realised that a quark is a bad example of a "small thing" since i don't know if it's believed to have a volume. But you get the idea anyway, i hope.

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    $\begingroup$ Some helpful things to look up in this context: no-hair theorem, cosmic censorship hypothesis, Kerr-Newman metric solutions and their toroidal distributions of mass (instead of a point). It is thought that every event horizon "hides" the mass distribution inside, revealing only the total mass; and that every singularity is going to be inside of an event horizon: with that said, the equations sometimes predict non-point-singularities inside the black hole so it makes some sense that there could be internal structure, and indeed there probably should be if black holes are formed by accretion. $\endgroup$ – CR Drost Oct 29 '15 at 12:58
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It is a misperception by (non-scientist) writers. The black hole physical model is a model based on General Relativity only. This tells something about real black holes, and have many interesting and complicated properties. Still, all scientists know that in the local conditions of very small scale and high density it is the realm of quantum mechanics, that don't accept such notion as point singularity. And the point is that nobody knows for now how to mix quantum mechanics and relativity, at least in these extreme conditions.

Now, whether "maths-like singularity" or "quantum-blurred" singularity, it is hidden inside the Schwarzschild sphere (which is indeed the "black hole"), so you will never know what happens inside, and it will never impact anything on the outside. So it will be difficult to experiment and test (and have "evidences" of anything inside), and indeed whatever you assume (e.g. "interior of black holes are made of cockroaches") will be compatible with correct physics outside. :-)

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  • $\begingroup$ Thanks. Does this mean then that General Relativity predicts an infinite density for black holes, but we know that GR doesn't apply to the small scale so we sort of ignore this part of it, knowing that it's just an artifact of the theory? $\endgroup$ – Max Williams Oct 29 '15 at 12:29
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    $\begingroup$ Yes. like many other zeros or asymptotic infinities in physics. These are math things, and maths are only locally isomorph to physics. God never divide by zero ;-p $\endgroup$ – Fabrice NEYRET Oct 29 '15 at 12:30
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    $\begingroup$ @MaxWilliams: in GR the singularity is not part of the universe. GR describes the universe as a mathematical structure called a manifold, and the singularity is excluded from the manifold. GR does not predict what happens at the singularity, only what happens when you get infinitessimally close to it. $\endgroup$ – John Rennie Oct 29 '15 at 12:41

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