# Phase transitions and geothermodynamics of black holes in dRGT massive gravity

## TL;DR

This paper explores the thermodynamics and phase transitions of black holes in dRGT massive gravity, revealing critical behavior and stability conditions through thermodynamical geometry and extended phase space analysis.

## Contribution

It introduces a new thermodynamic first law including graviton mass as a variable and analyzes critical phenomena in black holes within dRGT massive gravity.

## Key findings

- Identification of two critical points in black hole thermodynamics.
- Correlation of Ricci scalar singularities with thermodynamic capacities.
- Influence of spacetime parameters on black hole stability.

## Abstract

In this paper, we study the thermodynamics and geothermodynamics of spherical black hole solutions in dRGT massive gravity in a new extended phase space. Inspired by the work of Kastor et al. [1], by interpreting the graviton mass as a thermodynamical variable, we propose a first law of thermodynamics which include a mass term and establish a new Smarr Formula. Then, we perform a thermodynamical analysis to reveal the existence of a critical behavior for black holes in dRGT massive gravity with two different critical points through canonical and grand canonical ensembles. To consolidate these results, we make use of the thermodynamical geometry formalism, with the HPEM and the Gibbs free energy metrics, to derive the singularities of Ricci scalar curvatures and show that they coincide with those of the capacities. The effect of different values of the spacetime parameters on the stability conditions is also discussed.