Phase transition of charged black holes in massive gravity through new methods

TL;DR

This paper explores the phase transitions and stability of charged black holes in massive gravity, examining how parameters like mass, charge, and topology influence thermodynamic behavior using both canonical and geometrical approaches.

Contribution

It introduces a comprehensive analysis of black hole phase transitions in massive gravity, highlighting the effects of massive parameters, boundary topology, and higher dimensions on thermodynamics.

Findings

Massive parameters significantly affect stability conditions.

Boundary topology influences thermodynamic behavior.

Geometrical thermodynamics effectively studies phase transitions.

Abstract

Motivated by providing preliminary steps to understand the conception of quantum gravity, in this paper, we study the phase structure of a semiclassical gravitational system. We investigate the stability conditions and phase transition of charged black holes in massive gravity via canonical and geometrical thermodynamic approaches. We point out the effects of massive parameter on stability conditions of these black holes and show how massive coefficients affect the phase transition points of these black holes. We also study the effects of boundary topology on thermodynamical behavior of the system. In addition, we give some arguments regarding the role of higher dimensions and highlight the effect of the electric charge in thermodynamical behavior. Then, we extend our study to geometrical thermodynamic approach and show that it can be a successful method for studying the black hole phase transition. At last, by employing the relation between thermodynamical pressure and cosmological constant, critical behavior of the system and the effects of different parameters on critical values are investigated.