[raylad]

Given that there is no absolute position in spacetime and everything is relative, in what sense is a black hole "spinning"?

Can't we just pick as a reference the black hole, and say that the everything else is spinning, just as well?

[pdonis]

> in what sense is a black hole "spinning"?

There are several equivalent ways of stating it:

(1) The hole's spacetime geometry is axisymmetric but not spherically symmetric;

(2) The hole has a Killing vector field that is timelike at infinity but is not hypersurface orthogonal;

(3) The hole has nonzero angular momentum as viewed in the asymptotically flat region at infinity.

> Can't we just pick as a reference the black hole, and say that the everything else is spinning, just as well?

No. All three of the above conditions are invariant and only depend on the spacetime geometry; they are unaffected by any choice of coordinates or the motion of any outside observers.

[adastra22]

No, spinning is an accelerated reference frame. If you spin on a carousel, you won’t feel the same as standing still.

Now what does it mean for a black hole, which we assume to be a singularity occupying no space at all, to be spinning? We don’t know. That’s one of the gaps in our theory. But as the collapsed remnants of an object that was spinning, they should have done residual angular momentum.

[pdonis]

> spinning is an accelerated reference frame

Not necessarily. The three definitions for a "spinning" black hole that I gave upthread do not require the presence of any accelerated frames or observers.

> what does it mean for a black hole, which we assume to be a singularity occupying no space at all

This is not correct. A black hole is a finite region of spacetime enclosed by an event horizon. The singularity is inside the hole but is not all of the hole.

> to be spinning? We don’t know.

Yes, we do. We have known since the 1960s that the Kerr solution to the Einstein Field Equation describes a spinning black hole, and all of the geometric properties of that solution have been known for almost as long as that.

> That’s one of the gaps in our theory.

No, it's not. See above.

> as the collapsed remnants of an object that was spinning, they should have done residual angular momentum.

This is correct, but it does not imply or support your other claims.

[adastra22]

You're missing the point that none of the three definitions you provided offer a mechanistic explanation.

[pdonis]

You're missing the point that, since a black hole is purely made of spacetime geometry, there is no "mechanistic explanation" of its spin in the sense you mean.

[adastra22]

You don't know that.

[georgyo]

Not a physicist, but no.

An object can spin relative to itself. Particles away from the center are constantly accelerating. Gravity or physical connection are the forces that prevent these particles from flying away.

Thinking about it, I am not even sure an object can spin relative to another object. Orbit sure, but not spin.

[pdonis]

> An object can spin relative to itself. Particles away from the center are constantly accelerating. Gravity or physical connection are the forces that prevent these particles from flying away.

This is a reasonable description of spin for an ordinary object, but it can't be used for a black hole, because a black hole is a vacuum solution; it has no "particles". See my other post upthread for better ways to view spin for a black hole.

> I am not even sure an object can spin relative to another object. Orbit sure, but not spin.

The usual definition of "spin" makes use of the object's center of mass frame, yes. Orbital angular momentum is thus separated out.

Note, though, that strictly speaking, in relativity there is no invariant way to make this split. It works very well as an approximation for most objects (like planets and stars), but there are complications when one tries to apply it to things like black holes. That's one reason why physicists prefer other ways of defining "spinning" for black holes that don't involve any split between orbital and spin angular momentum.