Coexistence curve and molecule number density of AdS topological charged black hole in massive gravity

Abstract

The coexistence curve and molecule number density of a 4-dimensional AdS topological charged black hole in massive gravity is investigated. We find that the analytic expression of the coexistence curve in the reduced parameter space is dependent on theory parameters. This is very different from the previous results obtained in other modified gravity such as $f(R)$ gravity and Gauss-Bonnet gravity. Besides, we derive the explicit expression of the physical quantity which describes the difference of the number densities of AdS topological charged black hole molecules between the small and large black hole. It is observed that the difference of the molecule number densities is also dependent on theory parameters. Both the expressions of the coexistence curve and the difference of the molecule number densities can be reduced into a form which is similar to a RN-AdS black hole if the mass of graviton $m$ is zero. Moreover, we find the shifted temperature under massive gravity. This can highlight the important role played by the mass of graviton and other parameters in the phase transitions of AdS black holes in massive gravity.

arXiv comment11 pages, 4 figures. arXiv admin note: text overlap with arXiv:1604.07931, arXiv:1506.03578 by other authors

References in corpus (16)

• Resummation of Massive Gravity
• P-V criticality of charged AdS black holes
• Generalization of the Fierz-Pauli Action
• Theoretical Aspects of Massive Gravity
• Resolving the Ghost Problem in non-Linear Massive Gravity
• Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization
• 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
• Insight into the Microscopic Structure of an AdS Black Hole from Thermodynamical Phase Transition
• Thermodynamics of Black Holes in Massive Gravity
• Thermodynamic Volumes and Isoperimetric Inequalities for de Sitter Black Holes
• Smarr Formula and an Extended First Law for Lovelock Gravity
• Triple points and phase diagrams in the extended phase space of charged Gauss-Bonnet black holes in AdS space
• van der Waals like behaviour of topological AdS black holes in massive gravity
• Aspects of massive gravity