Black hole scalar hair in asymptotically anti-de Sitter spacetimes -: art. no. 024038

The unexpected discovery of hairy black hole solutions in theories with scalar fields simply by considering asymptotically anti-de Sitter (AdS) space, rather than asymptotically flat boundary conditions is analyzed in a way that exhibits in a clear manner the differences between the two situations. It is shown that the trivial Schwarzschild-anti-de Sitter space becomes unstable in some of these situations, and the possible relevance of this fact for the AdS conformal field theory conjecture is pointed out.