Black Holes with Scalar Hair and Asymptotics in N=8 Supergravity

We consider N=8 gauged supergravity in four and five dimensions. We find the asymptotic anti-de Sitter (AdS) symmetry group is preserved for a class of weakened boundary conditions on the metric and on scalars with sufficiently negative mass squared. Each such scalar gives rise to a one-parameter family of AdS-invariant boundary conditions, in which the metric falls off slower than usual. The generators of the asymptotic symmetries are finite, but generically acquire a contribution from the scalars. We discuss how these generalized AdS boundary conditions can be incorporated in the AdS/CFT correspondence. For a large class of boundary conditions we numerically find a one-parameter family of black hole solutions with scalar hair. These black holes exist above a certain critical mass and are disconnected from the Schwarschild-AdS black hole, which is a solution for all boundary conditions. The hairy black holes lift to inhomogeneous black brane solutions in ten or eleven dimensions