Hairy Black Holes in Massive Gravity: Thermodynamics and Phase Structure

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.

12 pages, 11 figures, relevant references added, match the published version

References in corpus (13)

• Resummation of Massive Gravity
• Gravitational Waves from Warped Spacetime
• Spontaneous breaking of Lorentz invariance, black holes and perpetuum mobile of the 2nd kind
• A Confining Strong First-Order Electroweak Phase Transition
• Lorentz Breaking Massive Gravity in Curved Space
• Charged Black Hole in a Canonical Ensemble
• Warped Deformed Throats have Faster (Electroweak) Phase Transitions
• Black Hole Thermodynamics and Massive Gravity
• Bumpy black holes from spontaneous Lorentz violation
• Stars and (Furry) Black Holes in Lorentz Breaking Massive Gravity
• Multi-String Theories, Massive Gravity and the AdS/CFT Correspondence
• Spontaneous Lorentz Violation, Negative Energy and the Second Law of Thermodynamics
• Gravitational Lorentz Violation and Superluminality via AdS/CFT Duality