Thermodynamically stable asymptotically flat hairy black holes with a dilaton potential: the general case

TL;DR

This paper demonstrates that in Einstein-Maxwell-dilaton theory, a broad class of asymptotically flat hairy black holes are thermodynamically and dynamically stable, with stability linked to the dilaton potential's behavior.

Contribution

It extends previous analysis by showing the existence of thermodynamically stable hairy black holes with a general dilaton potential, including their dynamical stability under perturbations.

Findings

Existence of thermodynamically stable hairy black holes with a general dilaton potential.

Stable solutions have a well-defined extremal limit.

Thermally stable solutions are also dynamically stable under spherical perturbations.

Abstract

We extend the analysis, initiated in arXiv:1901.01269, of the thermodynamic stability of four-dimensional asymptotically flat hairy black holes by considering a general class of exact solutions in Einstein-Maxwell-dilaton theory with a non-trivial dilaton potential. We find that, regardless of the values of the parameters of the theory, there always exists a sub-class of hairy black holes that are thermodynamically stable and have the extremal limit well defined. This generic feature that makes the equilibrium configurations locally stable should be related to the properties of the dilaton potential that is decaying towards the spatial infinity, but behaves as a box close to the horizon. We prove that these thermodynamically stable solutions are also dynamically stable under spherically symmetric perturbations.