Black holes with scalar hair and asymptotics in A = 8 supergravity

We consider N = 8 gauged supergravity in D = 4 and D = 5. We show one can weaken the boundary conditions on the metric and on all scalars with m ² < -(D-1)²/4 - 1 while preserving the asymptotic anti-de Sitter (AdS) symmetries. Each scalar admits a oneparameter family of AdS-invariant boundary conditions for which the metric falls off slower than usual. The generators of the asymptotic symmetries are finite, but generically acquire a contribution from the scalars. For a large class of boundary conditions we numerically find a one-parameter family of black holes with scalar hair. These solutions exist above a certain critical mass and are disconnected from the Schwarschild-AdS black hole, which is a solution for all boundary conditions. We show the Schwarschild-AdS black hole has larger entropy than a hairy black hole of the same mass. The hairy black holes lift to inhomogeneous black brane solutions in ten or eleven dimensions. We briefly discuss how generalized AdS-invariant boundary conditions can be incorporated in the AdS/CFT correspondence.