Quantum corrected thermodynamics of nonlinearly charged BTZ black holes in massive gravity's rainbow

TL;DR

This paper investigates the quantum-corrected thermodynamics of nonlinearly charged BTZ black holes within massive gravity's rainbow, revealing phase transitions and stability changes due to quantum effects.

Contribution

It introduces quantum corrections to black hole thermodynamics in massive gravity's rainbow with nonlinear electrodynamics, highlighting new phase transition phenomena.

Findings

Quantum corrections induce second-order phase transitions.

Modified first law of thermodynamics with logarithmic entropy corrections.

Quantum effects influence black hole stability and phase structure.

Abstract

In this paper, we consider three-dimensional massive gravity's rainbow and obtain black hole solutions in three different cases of Born-Infeld, logarithmic, and exponential theories of nonlinear electrodynamics. We discuss the horizon structure and geometrical properties. Then, we study thermodynamics of these models by considering the first-order quantum correction effects, which appears as a logarithmic term in the black hole entropy. We discuss such effects on the black hole stability and phase transitions. We find that, due to the quantum corrections, the second-order phase transition happens in Born-Infeld and logarithmic models. We obtain the modified first law of black hole thermodynamics in the presence of logarithmic corrections.