On the thermodynamics of hairy black holes

TL;DR

This paper studies the thermodynamic properties of a broad class of asymptotically AdS hairy black holes, revealing phase transitions and stability characteristics similar to classical black hole solutions.

Contribution

It provides a detailed thermodynamic analysis of hairy black holes, including phase transition behavior, using Hamiltonian and counterterm methods, which was not previously explored.

Findings

Existence of small and large hairy black holes at fixed temperature

Large hairy black holes have positive specific heat and stability

Identification of first order phase transitions akin to Hawking-Page transition

Abstract

We investigate the thermodynamics of a general class of exact 4-dimensional asymptotically Anti-de Sitter hairy black hole solutions and show that, for a fixed temperature, there are small and large hairy black holes similar to the Schwarzschild-AdS black hole. The large black holes have positive specific heat and so they can be in equilibrium with a thermal bath of radiation at the Hawking temperature. The relevant thermodynamic quantities are computed by using the Hamiltonian formalism and counterterm method. We explicitly show that there are first order phase transitions similar to the Hawking-Page phase transition.