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Phase equilibrium and microstructure of topological AdS black holes in massive gravity

In order to clearly understand the gravitational theory through the thermal properties of the black hole, it is important to further investigate the first-order phase transition of black holes. In this paper, we adopt different conjugate variables ( , , , and ) and apply Maxwell's equal-area law to study the phase equilibrium of a topological black hole in massive gravity. The condition and latent heat of phase transition are displayed as well as the coexistent curve of . The result shows that the phase transition of this system is the high/low electric potentials one, not only the large/small black holes one. We also analyze the effect of the model's parameters on phase transition. Furthermore we introduce a new order parameter to probe the microstructure of this system. This work will provide the theoretical basis to study the phase structure of topological black holes in massive gravity and to further explore the gravitational theory.