First of all, there's a hard upper limit on how fast a black hole can rotate (more specifically on how much angular momentum it can have), past which the equations stop making physical sense. At this angular momentum, the event horizon surface of the rotating black hole is substantially smaller than the event horizon for a correspondingly massive non-rotating black hole, which is a strange concept on its own.
Also, while non-rotating black holes have a point-like singularity at their heart,* in order to allow any sort of rotation, the singularity at the center of a rotating black hole is instead an infinitesimally thin ring with finite radius.
Then there's the ergosphere, which is an ellipsoidal region outside the Schwartzchild radius in which material is forced to rotate at the same rate as the black hole itself. This is because the so-called 'fabric' of spacetime is being dragged along with the black hole's rotation, at a rate faster than the speed of light to an outside observer! That means that at the outer edge of the ergosphere, it is possible for a photon to be traveling along the edge at the speed of light relative to spacetime, but appear stationary to an observer watching from outside. Weird, eh?
* This is a result of general relativity (as are most things to do with black holes). Basically inside the Schwartzchild radius of a black hole, space becomes timelike. There are a few ways of looking at that. The most simplistic one (not to say it's not the most correct - I'm not claiming to be a GR expert) is that time in the normal universe goes only one way. You don't have any choice in what direction you go through time, or how fast you do so - you are guaranteed to experience one second per second (in your local coordinates, in any case). Similarly, once you pass the event horizon of a black hole, the extreme curvature of spacetime means that there's only one way you can go: inwards. And with the amount of mass black holes contain, it is believed to be impossible to maintain enough outward pressure to support any spacial extent of the mass inside. It has to all condense into a single point at the very center, which is called a singularity. At this point, quantum gravity hits, and we have no clue what is going on.
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