definition of "black hole" for the purposes of no-hair theorems? Living Reviews has a nice review article on no-hair theorems: http://www.livingreviews.org/lrr-1998-6 Their rough verbal statement of the no-hair theorem for GR coupled to E&M is: "all stationary black hole solutions to the EM equations (with non-degenerate horizon) are parametrized by their mass, angular momentum and electric charge." I have a really elementary question, which is how "black hole" is defined in this context. Maybe I'm missing it, but I don't see anywhere in the Living Reviews article where they come out and say this plainly. It seems to me that it can't be "a black hole is any electrovac solution with a singularity," because then the proof of the no-hair theorem would seem to be a proof of cosmic censorship in the case of GR+EM, which I assume has not been proved...? Is [itex]\Lambda=0[/itex] assumed? For the purposes of this theorem, does "black hole" include things like topological defects? Is it explicitly limited to things that have an event horizon? How about things that aren't asymptotically flat?