Holographic Lovelock gravities and black holes

Abstract

We study holographic implications of Lovelock gravities in AdS spacetimes. For a generic Lovelock gravity in arbitrary spacetime dimensions we formulate the existence condition for asymptotically AdS black holes. We consider small fluctuations around these black holes and determine the constraint on Lovelock parameters by demanding causality of the boundary theory. For the case of cubic Lovelock gravity in seven spacetime dimensions we compute the holographic Weyl anomaly and determine the three point functions of the stress energy tensor in the boundary CFT. Remarkably, these correlators happen to satisfy the same relation as the one imposed by supersymmetry. We then compute the energy flux; requiring it to be positive is shown to be completely equivalent to requiring causality of the finite temperature CFT dual to the black hole. These constraints are not stringent enough to place any positive lower bound on the value of viscosity. Finally, we conjecture an expression for the energy flux valid for any Lovelock theory in arbitrary dimensions.