Hairy black holes, scalar charges and extended thermodynamics

TL;DR

This paper investigates scalar charges in stationary spacetimes, establishing conditions for black hole solutions with scalar hair, and explores their thermodynamics, including a first law and Smarr formula, exemplified by the Anabalón-Oliva black hole.

Contribution

It introduces new conditions on scalar potentials for static black holes with scalar hair and extends thermodynamic laws to these hairy black holes.

Findings

Derived conditions for scalar potentials allowing hairy black holes.

Established a first law and Smarr relation for extended thermodynamics.

Analyzed the Anabalón-Oliva hairy black hole as an example.

Abstract

We explore the use of the recently defined scalar charge which satisfies a Gauss law in stationary spacetimes, in the context of theories with a scalar potential. We find new conditions that this potential has to satisfy in order to allow for static, asymptotically-flat black-hole solutions with regular horizons and non-trivial scalar field. These conditions are equivalent to some of the known ``no-hair'' theorems (such as Bekenstein's). We study the extended thermodynamics of these systems, deriving a first law and a Smarr formula. As an example, we study the Anabal\'on-Oliva hairy black hole