Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2012-03-19
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
12 pages, 11 figures
Scientific paper
The thermodynamic properties of a static and spherically-symmetric hairy black hole of massive gravity 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 thermal energy and entropy, and we study 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.
Capela Fabio
Nardini Germano
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