I guess nobody really knows the true nature of black holes, however, based on everything I know about black holes, there is a "singularity" at their center, which has finite mass but is infinitely small and thus infinitely dense. So a black hole is really just a point mass that dramatically warps the space-time around it so that an event horizon is achieved.
What doesn't make sense to me is how a true mathematical "point" can rotate, or at least how it is even possible to determine if a point is rotating (or if it should even make a difference about whether or not it is rotating, for the same reason it would be impossible to tell if a perfect, featureless sphere were rotating (I know it would have higher rotational energy but lets assume you can't measure that because a true "point" can't attain rotational energy since it has no radius)).
The only conceptual solution I have to describe a rotating black hole would be to compare it to a rotating whirlpool, where the surface of the water is the fabric of space-time… but this is different because there is no "singularity" in a whirlpool that causes the water around it to rotate, whirlpools form from flow of water around a point (put into motion perhaps by some kid swirling water in a 2-liter bottle… it's due to an external cause), but the only thing that could cause rotation around a black hole would be the singularity itself, which doesn't make sense because, once again, how can we know if a true point is actually rotating?
Aside from everything I've said, here is what I am actually asking: Why/how do some black holes rotate… what is the mechanism of their rotation (is analogous to a spinning point or a 3-d whirlpool, or something different)?
Best Answer
They rotate because they are produced by matter that has net angular momentum, and angular momentum is conserved in axially symmetric space-time. So, there's nothing unusual making them rotate that's different from any other physics.
However, you are absolutely right to object that rotation of an infinitesimally small point wouldn't make much sense. In quantum mechanics, we talk about infinitesimally small particles having intrinsic angular momentum ("spin") but this is a uniquely quantum effect and General Relativity is a classical theory. So, your question is a good one. Fortunately, it has a simple answer: the singularity of a rotating black hole in GR is not a point, it's a ring around the black hole's axis of rotation. A rotating ring - even an infinitesimally small one - is sensible because it's topologically distinct from a zero dimensional point.
As a side note, physicists don't tend to believe singularities are real. The general feeling is that quantum gravity will turn them into something more physical. However, it is at least reassuring that GR still makes sense regardless.