# What evidence is there that infinities exist anywhere around or within a black hole?

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.

• 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. – CR Drost Oct 29 '15 at 12:58