Caption: Cartoon of a Kerr black hole.
Features:
Kerr black holes have mass and angular momentum, but zero net electric charge.
For brevity, one just says Kerr black hole for approximate Kerr black hole when talking of actual observed black hole.
Note that the more slowly rotating the Kerr black hole, the more closely it are approximates a Schwarzschild black hole and, in fact, to some degree all black holes can be approximated as Schwarzschild black holes
Note also that there are always astronomical perturbations, and so the black holes can only ever approach the ideal behavior of Kerr black holes and Schwarzschild black holes.
It was once thought that Kerr-Newman black holes were unlikely to actually exist, but since circa 2015 their existence has become more of a possibility.
The ring singularity is an infinitely thin, infinite point mass ring of mass.
Of course, neither kind of singularity is thought to exist since it is thought that quantum gravity must prevent collapse to singularities. But without an established quantum gravity theory, we do NOT have an established idea for what is the actual collapsed center of a black hole. But it probably has volume and might be an oblate spheroid or a toroid for a Kerr black hole.
There is a formula for the Kerr-Schwarzschild radius which is a generalization of the one for the Schwarzschild radius---but it's beyond our scope.
The ergosphere touches the event horizon rotation axis and is an oblate spheroid (as in the figure) for relatively low angular momentum and is a sort of symmetrical pumpkin shape for relatively high angular momentum (see Wikipedia: Ergosphere).
Well a Kerr black hole twists the spacetime around it, and so causes frame-dragging (AKA the Lense-Thirring effect).
The ergosphere is defined as that region where the frame-dragging is so strong that NO test particle in the ergosphere can be held stationary with respect to an outside observer.
Recall a test particle is an object sufficiently negligible in effect on the physical system external to itself that it does NOT affect said physical system. Among other things, a test particle has negligible mass-energy.
An object of finite mass-energy can resist being dragged if it has sufficient mass-energy to perturb the Kerr black hole structure.
But here, we will go no further.