Stability and Thermodynamics of AdS Black Holes with Scalar Hair

TL;DR

This paper investigates the stability and thermodynamics of novel AdS black holes with scalar hair, revealing their thermodynamic properties and inherent instabilities, and suggesting they are not the final state of evolution.

Contribution

It provides a detailed thermodynamic and stability analysis of scalar-hair AdS black holes, highlighting their properties and potential evolution pathways.

Findings

Schwarzschild-AdS is thermodynamically stable against decay into hairy black holes.

Hairy black holes exhibit an unstable radial fluctuation in both four and five dimensions.

Schwarzschild-AdS is likely not the endstate of the instability of hairy black holes.

Abstract

Recently a class of static spherical black hole solutions with scalar hair was found in four and five dimensional gauged supergravity with modified, but AdS invariant boundary conditions. These black holes are fully specified by a single conserved charge, namely their mass, which acquires a contribution from the scalar field. Here we report on a more detailed study of some of the properties of these solutions. A thermodynamic analysis shows that in the canonical ensemble the standard Schwarzschild-AdS black hole is stable against decay into a hairy black hole. We also study the stability of the hairy black holes and find there always exists an unstable radial fluctuation, in both four and five dimensions. We argue, however, that Schwarzschild-AdS is probably not the endstate of evolution under this instability.