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

TL;DR

This paper explores how weakening boundary conditions in N=8 supergravity allows for new black hole solutions with scalar hair, affecting asymptotic symmetries and entropy, with implications for AdS/CFT correspondence.

Contribution

It demonstrates the existence of scalar-hairy black holes under relaxed boundary conditions in N=8 supergravity, extending previous solutions and analyzing their properties.

Findings

Existence of scalar-hairy black holes above a critical mass.

Hairy black holes have lower entropy than Schwarzschild-AdS black holes of the same mass.

Solutions lift to inhomogeneous black branes in higher dimensions.

Abstract

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 $m^2 <-{(D-1)^2 \over 4}+1$, while preserving the asymptotic anti-de Sitter (AdS) symmetries. Each scalar admits a one-parameter 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.