On black hole thermodynamics with a momentum relaxation

TL;DR

This paper explores the thermodynamics of black holes with scalar hair related to momentum relaxation, revealing unique thermodynamic behaviors and providing a unified understanding across different parameter regimes.

Contribution

It introduces a classification of black hole solutions with scalar hair and momentum relaxation, explaining their unusual thermodynamic features comprehensively.

Findings

Identification of a special point with discontinuous thermodynamic interpretation

Unified thermodynamic framework for black holes with momentum relaxation

Comparison with topological AdS black holes

Abstract

We investigate black hole thermodynamics involving a scalar hair which is dual to a momentum relaxation of the dual field theory. This black hole geometry is able to be classified by two parameters. One is a momentum relaxation and the other is a mass density of another matter localized at the center. Even though all parameters are continuous, there exists a specific point where its thermodynamic interpretation is not continuously connected to the one defined in the other parameter regime. The similar feature also appears in a topological AdS black hole. In this work, we show why such an unusual thermodynamic feature happens and provide a unified way to understand such an exotic black hole thermodynamically in the entire parameter range.