Thermodynamic instability of charged dilaton black holes in AdS spaces

TL;DR

This paper investigates the thermodynamic stability of charged dilaton black holes in AdS spaces, revealing how the dilaton coupling affects their thermal stability and identifying stable and unstable phases.

Contribution

It provides a detailed stability analysis of charged dilaton black holes in AdS, including a new Smarr-type formula and the impact of the dilaton coupling on stability.

Findings

Black holes are stable for small dilaton coupling constant.

Large dilaton coupling leads to thermodynamic instability.

The study offers insights into the phase structure of dilaton black holes.

Abstract

We study thermodynamic instability of a class of $(n+1)$-dimensional charged dilaton black holes in the background of anti-de Sitter universe. We calculate the quasilocal mass of the AdS dilaton black hole through the use of the subtraction method of Brown and York. We find a Smarr-type formula and perform a stability analysis in the canonical ensemble and disclose the effect of the dilaton field on the thermal stability of the solutions. Our study shows that the solutions are thermally stable for small $\alpha$, while for large $\alpha$ the system has an unstable phase, where $\alpha $ is a coupling constant between the dilaton and matter field.