Phase transitions of black holes in massive gravity

Abstract

In this paper we have studied thermodynamics of a black hole in massive gravity in the canonical ensemble. The massive gravity theory in consideration here has a massive graviton due to Lorentz symmetry breaking. The black hole studied here has a scalar charge due to the massive graviton and is asymptotically anti-de Sitter. We have computed various thermodynamical quantities such as temperature, specific heat and free energy. Both the local and global stability of the black hole are studied by observing the behavior of the specific heat and the free energy. We have observed that there is a first order phase transition between small and large black hole for a certain range of the scalar charge. This phase transition is similar to the liquid/gas phase transition at constant temperature for a Van der Waals fluid. The coexistence curves for the small and large black hole branches are also discussed in detail.

Accepted to be published in Modern Physics Letters A. Three more references added

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• Accretion of matter onto black holes in massive gravity with Lorentz symmetry breaking
• Thermodynamical stability of $f(R)$-AdS black holes in grand canonical ensemble
• Non-linear black holes in 2+1 dimensions as heat engines
• Massive gravity with Lorentz symmetry breaking: black holes as heat engines
• Thermodynamic geometry of static and rotating regular black holes in conformal massive gravity
• Extended Phase Space Thermodynamics of Black Holes in Massive Gravity
• Magnetic black holes in 4$D$ Einstein--Gauss--Bonnet massive gravity coupled to nonlinear electrodynamics
• Ruppeiner geometry, P-V criticality and interacting microstructures of black holes in dRGT massive gravity
• Thermodynamics and phase transitions of charged-AdS black holes in dRGT massive gravity with nonlinear electrodynamics
• Thermodynamics and the Joule-Thomson expansion of dilaton black holes in 2+1 dimensions