Rotating Black Hole: Is it Logical?

[cbd1]

Okay, I am somewhat perplexed by the theory of a rotating black hole.
I know that there is a solution of Einstein's equations that shows a black hole can be rotating mathematically, but I find it highly likely that this is a non-real solution.
Think about it. A black hole is a singularity, the tiniest point possible, surrounded by only a hollow area out to a radius which borders the edge, the event horizon. It seems to me that to say a black hole is rotating is to say that an empty area of space can be rotating.
A black hole is not like a body, say a star or planet, that has materials in motion spinning through inertia. With a black hole, there are no materials to have angular momentum. Even if you tried to say that the singularity is spinning (as that is where the mass is) it occupies zero space, so it is equally illogical to say that it can have angular momentum.

Further, the indirect evidence used to support rotating black holes, accretion disks and jets, seem to me just as likely that the materials are spinning around the black hole, not that the black hole is rotating.

 

[Marcellus]

I'm not quite sure why you say it's a hollow area. "Hollow" suggests you are referencing empty space. A black hole is highly compressed mass...compressed to a point of zero volume and infinite density. So, theoreticaly, that mass can still rotate.

 

[ZikZak]

Actually, the singularity of a rotating black hole is a ring, not a point.

And electrons are points with zero space that have angular momentum.

 

[cbd1]

ZikZak:

*If* a rotating black hole were possible, its singularity's wavefunction would be a ring. This is much different than a ring-shaped singularity.

And the electron *might* have zero size. It does not have to be so. On the other hand, the very definition of a singularity requires it to occupy zero space.

 

[Nabeshin]

So what, throw conservation of angular momentum out the window then? Claim it's somehow "expelled" during the collapse of a star? I think you'd be hard pressed to find such a mechanism.

In contrast to what you say, where kerr black holes are "non-physical", it's actually quite the opposite: a schwarzschild black hole is non-physical, whereas all black holes are kerr (since all stars have some angular momentum).

 

[cbd1]

I know why it was presumed that a black hole would have to rotate if it was formed from a rotating star.
I'm talking about the actual mechanism by which the rotation could be possible. How can something with zero dimension have angular momentum?

 

[Nabeshin]

Again, consider an electron.

If you want to argue "perhaps an electron doesn't really have zero size..." then you have to admit that GR is probably not fully qualified to describe spacetime at extremely high densities and small length scales. A full quantum gravity is needed, and perhaps such a theory does not predict the existence of a singularity.

 

[ZikZak]

*If* a rotating black hole were possible, its singularity's wavefunction would be a ring. This is much different than a ring-shaped singularity.

That is not what GR predicts. GR is a classical theory that has nothing to say about wave functions at all. No GR prediction ever contains the word "wavefunction." The singularity of a Kerr black hole is a ring. Not a wavefunction. A ring.

And the electron *might* have zero size. It does not have to be so. On the other hand, the very definition of a singularity requires it to occupy zero space.

Measured the electron's size, have you?

 

[stevebd1]

The rotation of a black hole is more about the rotation of space (i.e. frame dragging) though the ring singularity is considered to spin at c. This is backed up to some extent when you consider the equation for the spin parameter $a$ (which is in units of length) which is $a=J/mc$ which is basically a rearrangement of the equation for angular momentum, $J=vmr$ where v=c and r=a. I have seen papers show the ring singularity at this radius between the event and Cauchy horizon (though how that would be possible when in this shallow region space is temporal isn't explained, also, in Kerr metric, r=0 at the singularity edge)- http://www.lsw.uni-heidelberg.de/users/mcamenzi/GR_07.pdf" page 35. There's also the suggestion that length contraction comes into play which reduces the coordinate radius of the ring singularity to within the Cauchy horizon so that the event horizons stay more or less spherical, this might suggest that while the ring singularity isn't spinning at exactly c, it's spinning very close to the speed of light.

 

[Stingray]

How can something with zero dimension have angular momentum?

It's easy to write down pointlike stress-energy tensors with nonzero spin angular momentum in special relativity. You just introduce a term involving the angular momentum tensor contracted into a derivative of a delta function.

This is not a good model for a Kerr black hole, but it's an easy example that illustrates how objects confined to a point even in a very simple (flat!) spacetime can still have angular momentum.

 

[Dale]

*If* a rotating black hole were possible, its singularity's wavefunction would be a ring. This is much different than a ring-shaped singularity.

ZikZak is correct. GR is a classical theory, and since we don't have a quantum theory of gravity it doesn't make much sense to talk about a singularity's wavefunction. The singularity of a Kerr black hole is indeed a "ring singularity" which has a finite radius and infinitesimal thickness.

http://en.wikipedia.org/wiki/Ring_singularity