Thermodynamics and reentrant phase transition for logarithmic nonlinear charged black holes in massive gravity

TL;DR

This paper explores higher-dimensional black holes in massive gravity with logarithmic nonlinear electrodynamics, revealing complex phase structures, reentrant phase transitions, and thermodynamic stability properties.

Contribution

It introduces new exact solutions for topological black holes in massive gravity coupled with nonlinear electrodynamics and analyzes their thermodynamic phase behavior without extending phase space.

Findings

Black holes exhibit multi-horizons due to anti-evaporation effects.

The solutions satisfy the first law of thermodynamics and follow a generalized Smarr formula.

Reentrant phase transitions and zeroth order phase transitions are observed.

Abstract

We investigate a new class of $(n+1)$-dimensional topological black hole solutions in the context of massive gravity and in the presence of logarithmic nonlinear electrodynamics. Exploring higher dimensional solutions in massive gravity coupled to nonlinear electrodynamics is motivated by holographic hypothesis as well as string theory. We first construct exact solutions of the field equations and then explore the behavior of the metric functions for different values of the model parameters. We observe that our black holes admit the multi-horizons caused by a quantum effect called anti-evaporation. Next, by calculating the conserved and thermodynamic quantities, we obtain a generalized Smarr formula. We find that the first law of black holes thermodynamics is satisfied on the black hole horizon. We study thermal stability of the obtained solutions in both canonical and grand canonical ensembles. We reveal that depending on the model parameters, our solutions exhibit a rich variety of phase structures. Finally, we explore, for the first time without extending thermodynamics phase space, the critical behavior and reentrant phase transition for black hole solutions in massive gravity theory. We realize that there is a zeroth order phase transition for a specified range of charge value and the system experiences a large/small/large reentrant phase transition due to the presence of nonlinear electrodynamics.