Conceptual problem on black hole singularity

[assassinsdoc]

I've read that there's a point in a black hole where matter is infinitely dense. There is zero volume but infinite density.
How is it possible for something to have zero volume but have an infinite density at the same time?

 

[mfb]

I've read that there's a point in a black hole where matter is infinitely dense.

Probably not, but we don't know.

How is it possible for something to have zero volume but have an infinite density at the same time?

The combination of both is way better than a finite volume with infinite density (which would have an infinite mass). There is no fundamental problem with such a singularity, it's just our knowledge of physics that does not work there.

 

[Nugatory]

I've read that there's a point in a black hole where matter is infinitely dense. There is zero volume but infinite density.

That is the result that general relativity predicts - if you assume that general relativity applies at arbitrarily small distances and high arbitrarily high densities. We could just as reasonably take this result as a hint that general relativity doesn't apply under such extreme conditions and that we'll need to extend GR with some new physics to handle this problem.

Similar things have happened before. Newtonian mechanics works just fine until you try applying it to objects moving at speeds near that of light, and then you have to extend it with special relativity to handle those extreme velocities.

 

[mfb]

Similar things have happened before. Newtonian mechanics works just fine until you try applying it to objects moving at speeds near that of light, and then you have to extend it with special relativity to handle those extreme velocities.

Well, that's a bit different. Newtonian physics would work fine with arbitrary velocities - if there is a preferred reference frame. There is no theoretical issue with that theory, it just does not happen to be realized.

 

[Nugatory]

Well, that's a bit different. Newtonian physics would work fine with arbitrary velocities - if there is a preferred reference frame. There is no theoretical issue with that theory, it just does not happen to be realized.

Fair enough... I was a bit uncomfortable with that example for exactly that reason, then decided that it was close enough to make the point about the limits of applicability of a theory even though it's not quite the same... What would be better example?

 

[bapowell]

What would be better example?

The singularity in Coulomb's Law as r -> 0?

 

[Nugatory]

The singularity in Coulomb's Law as r -> 0?

D'oh. Thanks.