Thermal analysis of black hole in de Rham--Gabadadze--Tolley massive gravity in Barrow entropy framework

TL;DR

This paper explores the thermodynamics and phase transitions of a black hole in de Rham--Gabadadze--Tolley massive gravity using Barrow entropy, revealing stability conditions and geometric thermodynamic behaviors.

Contribution

It introduces a novel thermodynamic analysis of black holes in massive gravity with Barrow entropy, including phase transition and stability insights.

Findings

Identified Van der Waals-like phase transition.

Analyzed black hole stability via heat capacity and Gibbs free energy.

Explored thermodynamic curvature behaviors with multiple geometric methods.

Abstract

This study examines a recently hypothesized black hole solution in de Rham--Gabadadze--Tolley massive gravity. Firstly, we consider the negative cosmological constant as a thermodynamic pressure. We extract the thermodynamical properties such as Hawking temperature, heat capacity and Gibbs free energy using the Barrow entropy. We also obtain a new pressure associated to the perfect fluid dark matter and discuss the first-order van der Waals-like phase transition. This black hole's stability is investigated through specific heat and Gibbs free energy. Also, we analyze the thermodynamic curvatures behavior of black hole through geometry methods (Weinhold, Ruppeiner, Hendi-Panahiyah-Eslam-Momennia (HPEM), and geometrothermodynamics (GTD)).