Extended Phase Space Thermodynamics of Black Holes in Massive Gravity

Abstract

We study the extended phase space thermodynamics of black holes in massive gravity. Particularly, we examine the critical behaviour of this black hole using the extended phase space formalism. Extended phase space in a sense that in which the cosmological constant should be treated as a thermodynamic pressure and its conjugate variable as a thermodynamic volume. In this phase space, we derive the black hole equation of state, the critical pressure, the critical volume and the critical temperature at the critical point. We also derive the critical ratio of this black hole. Moreover, we derive the black hole reduced equation of state in terms of the reduced pressure, the reduced volume and the reduced temperature. Furthermore, we examine the Ehrenfest equations of black holes in massive gravity in the extended phase space at the critical point. We show that the Ehrenfest equations are satisfied of this black hole and the black hole encounters a second order phase transition at the critical point in the said phase space. This is re-examined by evaluating the Pregogine-Defay ratio~($\Pi$). We determine the value of this ratio is $\Pi =1$. The outcome of this study is completely analogous to the nature of liquid-gas phase transition at the critical point. This investigation also further gives us the profound understanding between the black hole of massive gravity with the liquid-gas system.

arXiv commentAccepted for publication in Modern Physics Letters A (MPLA)

References in corpus (20)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• 4D Gravity on a Brane in 5D Minkowski Space
• P-V criticality of charged AdS black holes
• Charged AdS Black Holes and Catastrophic Holography
• Enthalpy and the Mechanics of AdS Black Holes
• Massive Gravity
• Theoretical Aspects of Massive Gravity
• Massive Gravity in Three Dimensions
• Holography, Thermodynamics and Fluctuations of Charged AdS Black Holes
• Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume
• Pressure and volume in the first law of black hole thermodynamics
• The cosmological constant and the black hole equation of state
• Extended phase space thermodynamics and P-V criticality of black holes with nonlinear source
• Thermodynamics of Reissner-Nordstrom-anti-de Sitter black holes in the grand canonical ensemble
• A unified picture of phase transition: from liquid-vapour systems to AdS black holes
• Charged black holes in nonlinear massive gravity
• P-V criticality in AdS black holes of massive gravity
• Black hole solutions in massive gravity
• Stars and (Furry) Black Holes in Lorentz Breaking Massive Gravity
• Phase transitions of black holes in massive gravity

Cited by in corpus (1)

• Thermodynamic Topological Classifications of Well-Known Black Holes