To baldly go where no man went before
Posted by Robert H.
In his reference frame, Lubos reports on a seminar by Reall on higher dimensional black holes and black rings and mentions that they violate a possible no hair theorem.
In addition to what he says there, even in 4D, if you go beyond Einstein-Maxwell by including non-abelian gauge groups, there are different solutions whose difference decays exponentially if you go to infinity and thus are not distinguished by ADM type charges. Thus, in Einstein-YM, there is hair even in 4D.
I would like to kick off a discussion of what we should make of this. Is the no hair theorem just a coincidence of a small class of theories or does it have a fundamental meaning or relevance (as for example cosmic censorship, a violation of which would have bad consequences for predictability)?
If you want to discuss a larger class of theorems, you can follow V. GATES, Empty KANGAROO, M. ROACHCOCK, and W.C. GALL in Stuperspace where they mention
“a black hole has no hair (the `Fuzzy Wuzzy’ theorem), you can’t comb the hair on a billiard ball, you can’t lasso a basketball, you can’t peel an orange without breaking the skin, you can’t make an omelet without breaking eggs, you can’t push a rope, you can’t roller-skate in a buffalo herd, and you can’t take a shower in a parakeet’s cage.”
Horowitz-Reall
In this context, you might want to have a look at my post about Horowitz and Reall. They provide evidence that things may not be as bad as you think. Higher-dimensional black holes may have hair, but perhaps only a finite amount of hair.