Hairy Black Holes in Massive Gravity: Thermodynamics and Phase Structure

TL;DR

This paper studies the thermodynamics and phase transitions of hairy black holes in massive gravity, revealing a phase structure similar to Reissner-Nordstrom black holes and identifying conditions for stability and phase transitions.

Contribution

It introduces a detailed thermodynamic analysis of hairy black holes in massive gravity, highlighting their phase structure and stability conditions.

Findings

Phase structure resembles Reissner-Nordstrom black holes.

Existence of a line of first-order phase transitions.

Long-lived small black holes may impact cosmological energy density.

Abstract

The thermodynamic properties of a static and spherically symmetric hairy black hole solution arising in massive gravity with spontaneous Lorentz breaking are investigated. The analysis is carried out by enclosing the black hole in a spherical cavity whose surface is maintained at a fixed temperature $T$. It turns out that the ensemble is well-defined only if the "hair" parameter $Q$ characterizing the solution is conserved. Under this condition we compute some relevant thermodynamic quantities, such as the thermal energy and entropy, and we study the stability and phase structure of the ensemble. In particular, for negative values of the hair parameter, the phase structure is isomorphic to the one of Reissner-Nordstrom black holes in the canonical ensemble. Moreover, the phase-diagram in the plan ($Q,T$) has a line of first-order phase transition that at a critical value of $Q$ terminates in a second-order phase transition. Below this line the dominant phase consists of small, cold black holes that are long-lived and may thus contribute much more to the energy density of the Universe than what is observationally allowed for radiating black holes.