John,

Basically, there are four exact black hole solutions, corresponding to combinations of mass(M), angular momentum(L) and electric charge (Q). Those are the only three "no hair" properties.

Schwarzschild is L = Q = 0. Kerr is the rotating black hole solution, L non-zero, but Q still 0. And then you get two more solutions for Q.

The interesting thing about Q and L is there are "naked singularity" solutions corresponding to the various ratios of Q/M and L/M. When those values exceed some point (probably unity in geometrical units, I think), you get naked singularities.

However, those aren't physical, because nothing with that much charge or L to mass ratio could gravitationally collapse on its own. You'd have to compress via external forces (which would exceed anything imaginable). On the L side, you can think of this as just spinning too fast for gravity to overcome the "centrifugal force".

That's part of Hawking's "cosmic censorhsip" conjecture -- no naked singularity solutions can physically form. No proof of that exists, and no one knows if naked singularities really are impossible or not.

-Richard