Charged BTZ black holes in the context of massive gravity's rainbow

TL;DR

This paper explores the thermodynamics and stability of charged BTZ black holes within massive gravity's rainbow, incorporating energy-dependent modifications to better understand their phase transitions and geometric thermodynamics.

Contribution

It introduces energy-dependent constants into massive gravity's rainbow to analyze thermodynamics and phase transitions of charged BTZ black holes in a novel framework.

Findings

Charged BTZ black holes exhibit specific thermodynamic behaviors.

Energy dependence influences stability and phase transition properties.

Geometrical thermodynamics approaches yield consistent insights.

Abstract

BTZ black holes are excellent laboratories for studying black hole thermodynamics which is a bridge between classical general relativity and quantum nature of gravitation. In addition, three-dimensional gravity could have equipped us for exploring some of the ideas behind the two dimensional conformal field theory based on the $AdS_{3}/CFT_{2}$. Considering the significant interests in these regards, we examine charged BTZ black holes. We consider the system contains massive gravity with energy dependent spacetime to enrich the results. In order to make high curvature (energy) BTZ black holes more realistic, we modify the theory by energy dependent constants. We investigate thermodynamic properties of the solutions by calculating heat capacity and free energy. We also analyze thermal stability and study the possibility of Hawking-Page phase transition. At last, we study geometrical thermodynamics of these black holes and compare the results of various approaches.