Black Holes: Volume & Forces Explored

[Invutil]

Do black hole singularities have 0 volume? What forces are keeping the particles from being in the same place?

 

[mfb]

What forces are keeping the particles from being in the same place?

If there is a singularity, none, and a singularity has a volume of 0 (otherwise it wouldn't be a singularity, at least not in our universe).
It is unclear if there is a singularity, as we don't have a proper unification of quantum physics and general relativity, and there both are relevant at the same time.

 

[bcrowell]

We just had a discussion of this: https://www.physicsforums.com/threa...s-equal-to-schwarzschild-radius.841320/unread

The brief answer is that in classical relativity, a singularity is not part of the spacetime manifold. It's not a point or a set of points. There is not even any straightforward way to define whether it's one-dimensional, two-dimensional, or three-dimensional. We certainly can't say whether or not it has volume, because that would require the use of the metric, and a singularity represents a breakdown of the metric.

This may be helpful: https://www.physicsforums.com/threads/boundary-construction-for-of-b-h-and-b-b-singularities.833399/

If there is a singularity, none, and a singularity has a volume of 0 (otherwise it wouldn't be a singularity, at least not in our universe).

This is wrong, for the reasons given above.

 

[mfb]

Hmm, right. It's probably better to say its volume is not well-defined.

 

[bcrowell]

Hmm, right. It's probably better to say its volume is not well-defined.

I would just say that there's no "it" whose volume we could even try to define. Classical GR doesn't describe a singularity as a physical or geometrical thing. Asking for physical characteristics of a singularity is like asking what time it is when the tip of the minute hand is at the center of the clock. The dial only exists around the circumference of the circle, not at its center. You might think that a black hole's mass, charge, and spin were properties attributable to the singularity, but GR doesn't actually describe them this way; they're properties of the whole spacetime that are only defined by an observer at asymptotic infinity.