I Where is the mass in a black hole?

[snorkack]

[This thread started as a hijack of https://www.physicsforums.com/threads/confusion-regarding-black-hole-spin.1079871/#post-7256289]

Are you sure that Schwarzschild black hole is best conceptualized as entirely vacuum, with no matter anywhere, rather than as a point mass at the point singularity, which is not quite ordinary matter but may count as extraordinary matter?

 

[Ibix]

Are you sure that Schwarzschild black hole is best conceptualized as entirely vacuum, with no matter anywhere, rather than as a point mass at the point singularity, which is not quite ordinary matter but may count as extraordinary matter?

Yes. The singularity is not a point (mass or otherwise), it's a space-like line that lies in the future of all worldlines entering the hole.

 

[PeterDonis]

Are you sure that Schwarzschild black hole is best conceptualized as entirely vacuum, with no matter anywhere

Yes. That's what the actual math says.

rather than as a point mass at the point singularity, which is not quite ordinary matter but may count as extraordinary matter?

No. That is not what the actual math says.

 

[Dale]

[This thread started as a hijack of https://www.physicsforums.com/threads/confusion-regarding-black-hole-spin.1079871/#post-7256289]

Are you sure that Schwarzschild black hole is best conceptualized as entirely vacuum, with no matter anywhere, rather than as a point mass at the point singularity, which is not quite ordinary matter but may count as extraordinary matter?

The Schwarzschild spacetime is the unique spherically symmetric vacuum spacetime.

Because it is the unique spherically symmetric vacuum spacetime, it does represent the spacetime in the vacuum outside of a spherically symmetric mass. So there are spacetimes that can be thought of as the Swarzschild spacetime surrounding matter.

But the maximally extended Schwarzschild spacetime cannot be understood that way. It is vacuum everywhere. It does not surround a singularity. It has a pair of singularities, one in the future and one in the past.

 

[PeterDonis]

it does represent the spacetime in the vacuum outside of a spherically symmetric mass. So there are spacetimes that can be thought of as the Swarzschild spacetime surrounding matter.

Just to be clear, there will be no singularity anywhere in such a spacetime, and the vacuum region will correspond to Schwarzschild spacetime outside of some areal radius $r$ (the areal radius of the surface of the matter), which must be at least 9/8 of the Schwarzschild radius corresponding to the mass of the matter.

 

[martinbn]

Yes. The singularity is not a point (mass or otherwise), it's a space-like line that lies in the future of all worldlines entering the hole.

Isn't it a space-like hypersurface?

 

[Ibix]

Isn't it a space-like hypersurface?

Surfaces of constant $r$ are hypercylinders of infinite length and cross-sectional area proportional to $r^2$. As $r\rightarrow 0$ the cross-sectional area goes to zero, which I would say means it is more like a 1d line than a surface. It's the singularity, though, so a 3d surface where two of the dimensions have zero extent is probably just as good a description...

As Peter pointed out the singularity is not part of the manifold, and singularities are the mathematical equivalent of "here be dragons" anyway. So mathematical descriptions may well not be as precise and unique as normal.

It isn't anything like a point in space, anyway, which would be a timelike line.

 

[javisot]

-GR black holes are typically vacuum solutions

-Being a vacuum solution to Einstein's equations means that stress-energy tensor is equal to zero. There is no matter anywhere, but there is curvature.

-A singularity in physics is the theory saying "you're asking me questions I'm not ready to answer".

-"Mass (or matter) is hidden in the singularity" is like saying that mass (or matter) is nowhere; the singularity is not just another point in the universe. Is not a point and it's not part of the manifold.

 

[PeroK]

I would put things in slightly more sober terms:

1) There is a vacuum solution to the EFE (Einstein Field equations), which is characterised by a parameter $M$, and is known as a Schwarzschild Black Hole. There is no stress-energy anywhere, although there is a singularity at $r = 0$.

2) The Schwarzschild Black Hole can also be used to describe the spacetime outside a spherically symmetric (non-spinning) object - but only outside the surface of the object. I.e. not all the way to $r = 0$.

3) If a star is sufficiently massive, then as it runs out of fuel, it will collapse and form a Schwarzschild black hole and an event horizon at the characteristic Schwarzschild radius. Although some of the star's mass will have been ejected in the collapse (supernova explosion), much of it will disappear below the event horizon.

4) What happens below the event horizon is a matter of conjecture. There is no known force that could resist the complete gravitational collapse of the star, which means the current theory of GR leads to a singularity at $r = 0$ and an incomplete description of what happens to the mass.

5) Alternatively, a theory of quantum gravity may describe more fully what happens to the mass of a collapsed star below the event horizon.