Can a Black Hole Have Angular Momentum?

[Identity]

A black hole is a singularity at which the curvature of spacetime becomes infinite. I understand that when a star collapses it can have a net angular momentum, but when it collapses down to a 0-dimensional singularity, what does it mean for that to have angular momentum?

Thanks

 

[Passionflower]

A black hole is a singularity at which the curvature of spacetime becomes infinite. I understand that when a star collapses it can have a net angular momentum, but when it collapses down to a 0-dimensional singularity, what does it mean for that to have angular momentum?

Thanks

A black hole is more than just the singularity. There is curvature stretching out to infinity. This curvature is different from that of a non-rotating black hole.

 

[Identity]

So basically what you're saying is that the fabric of 'spacetime' is spinning?

It just seems weird to me because for a schwarzschild black hole, it's the mass of the singularity that distorts spacetime.
But for a spinning black hole, the spinning of spacetime is not 'caused' by the singularity (it can't be, because the singularity doesn't spin), but is intrinsic to the fabric? What would happen if the singularity suddenly disappeared? Would we be left with a random vortex in spacetime?

 

[Ben Niehoff]

The singularity of a Kerr black hole (i.e., a black hole with angular momentum) is not point-like. It is ring-shaped.

 

[PeterDonis]

It just seems weird to me because for a schwarzschild black hole, it's the mass of the singularity that distorts spacetime.

Actually, strictly speaking, it isn't. A real black hole is formed by the collapse of a massive object, and the distortion of spacetime that looks to us like "gravity" pulling us towards the black hole, is actually caused by the matter in the collapsing object while it was collapsing. That matter leaves an "imprint" on spacetime as it collapses, and the imprint is what we see as the black hole's gravitational field.

This picture generalizes easily to the case of a spinning black hole; it is formed by the collapse of a spinning object, and the "imprint" left by such an object on spacetime as it collapses contains "spin" as well as "mass".

 

[Passionflower]

That matter leaves an "imprint" on spacetime as it collapses, and the imprint is what we see as the black hole's gravitational field.
...
the "imprint" left by such an object on spacetime as it collapses contains "spin" as well as "mass".

I have trouble agreeing with you on this.

"Weyl" curvature comes from neighboring curvature and changes spread with the speed of light.

 

[PeterDonis]

I have trouble agreeing with you on this.

"Weyl" curvature comes from neighboring curvature and changes spread with the speed of light.

Yes, which means that the Weyl curvature around a black hole, which appears to us as its gravity, can't be coming from inside the horizon, because then it would have to spread faster than light. And in the vacuum region outside the horizon, the Weyl curvature is static; it doesn't change with time. So for it to have come into being in the first place, it must be coming from a "source" inside the past light cone of any event outside the horizon, and the only source that's there is the collapsing object that formed the hole.

It's true that this reasoning does not apply to an "eternal" black hole that is not formed by a collapsing object, but those are generally considered "unphysical", and the fact that there is no way for their Weyl curvature to come into being is one reason why.