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

TL;DR

This paper analyzes the phase transition properties of 4D AdS topological charged black holes in massive gravity, revealing how theory parameters influence the coexistence curve and molecule number density differences, with implications for black hole thermodynamics.

Contribution

It provides explicit expressions for the coexistence curve and molecule number density differences in massive gravity, highlighting their dependence on theory parameters and contrasting with other modified gravity theories.

Findings

Coexistence curve depends on theory parameters in massive gravity.

Difference in molecule number densities varies with theory parameters.

Reduced forms resemble RN-AdS black holes when graviton mass is zero.

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.