Hairy Black Holes in Massive Gravity: Thermodynamics and Phase Structure

Understand

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.