Phase transitions of black holes in massive gravity

TL;DR

This paper explores the thermodynamics and phase transitions of anti-de Sitter black holes in massive gravity, revealing a Van der Waals-like first order phase transition between small and large black holes.

Contribution

It provides a detailed analysis of black hole thermodynamics in massive gravity with Lorentz symmetry breaking, highlighting phase transition behavior and stability conditions.

Findings

Identified a first order phase transition similar to Van der Waals fluid.

Analyzed stability through specific heat and free energy behavior.

Discussed coexistence curves for black hole phases.

Abstract

In this paper we have studied thermodynamics of a black hole in massive gravity in the canonical ensemble. The massive gravity theory in consideration here has a massive graviton due to Lorentz symmetry breaking. The black hole studied here has a scalar charge due to the massive graviton and is asymptotically anti-de Sitter. We have computed various thermodynamical quantities such as temperature, specific heat and free energy. Both the local and global stability of the black hole are studied by observing the behavior of the specific heat and the free energy. We have observed that there is a first order phase transition between small and large black hole for a certain range of the scalar charge. This phase transition is similar to the liquid/gas phase transition at constant temperature for a Van der Waals fluid. The coexistence curves for the small and large black hole branches are also discussed in detail.