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February 10, 2005

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.”

Posted at February 10, 2005 12:14 PM UTC

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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.

Posted by: Jacques Distler on February 10, 2005 3:30 PM | Permalink | PGP Sig | Reply to this

Solitonic vs perturbative

Is the no hair theorem just a coincidence of a small class of theories or does it have a fundamental meaning or relevance […]?

So why should be expect BHs to have little hair?

I guess it should be related to the correspondence between solitonic solutions and perturbative excitations.

Black holes/strings/branes can be regarded as the strongly coupled version of respective objects in perturbation theory. As such, they should not carry more hair than these perturbative excitations.

So in as far as BHs correspond to pointlike excitations the number of hair is rather limited. Once we move to black strings the number of degrees of freedom of the object as it appears in perturbation theory increase drastically and so does apparently that of the respective solitonic object.

Posted by: Urs on February 12, 2005 2:52 AM | Permalink | Reply to this

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