Thermodynamics and phase transitions of charged-AdS black holes in dRGT massive gravity with nonlinear electrodynamics

TL;DR

This paper explores the thermodynamic behavior and phase transitions of charged AdS black holes in dRGT massive gravity coupled with exponential nonlinear electrodynamics, revealing complex phase structures and critical phenomena.

Contribution

It introduces a new class of charged AdS black holes in dRGT massive gravity with exponential NED and systematically analyzes their thermodynamics and phase transitions.

Findings

Black holes exhibit van der Waals-like first-order phase transitions.

Presence of second-order critical points and reentrant phase transitions.

Rich thermodynamic phase structure depending on magnetic charge.

Abstract

Investigating black holes in modified theories of gravity offers fertile ground for exploring phenomena beyond the scope of general relativity. We investigate a novel class of charged anti-de Sitter (AdS) black holes within the ghost-free de Rham-Gabadadze-Tolley (dRGT) massive gravity, minimally coupled to an exponential form of nonlinear electrodynamics (NED). The NED sector is modelled by an exponential electrodynamics Lagrangian, which leads to singular black hole geometries in contrast to many regular configurations known in other NED models. In turn, we systematically investigate the thermodynamic properties and phase structure of the obtained black holes. The results show that the system has a rich thermodynamic structure. For different values of the magnetic charge $q$, the black hole can exhibit several types of phase transitions. These include van der Waals-like first-order phase transitions, second-order critical behavior, and a reentrant phase transition between small and large black holes without extending the phase space ($\Lambda=$constant). Our study enhances the understanding of AdS black holes in ghost-free massive gravity, providing further insights into the interplay between graviton mass and NED. The results highlight how the combined effects of graviton mass and electromagnetic nonlinearity can yield a rich and complex thermodynamic phase space, offering further insights relevant to the gauge/gravity duality and the ongoing search for observational signatures of modified gravity.