Black hole scalar hair in asymptotically anti–de Sitter spacetimes

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.