Exponential corrected thermodynamics of Born-Infeld BTZ black holes in massive gravity

TL;DR

This paper investigates how quantum entropy corrections, both logarithmic and exponential, affect the thermodynamics of Born-Infeld BTZ black holes in massive gravity, revealing impacts on phase transitions and free energy.

Contribution

It introduces a comparative analysis of logarithmic and exponential quantum corrections on black hole thermodynamics within massive gravity.

Findings

Exponential correction induces a second-order phase transition point.

Quantum corrections significantly influence the Helmholtz free energy of large black holes.

The equation of state exhibits a virial expansion at leading order.

Abstract

It is known that entropy of black hole gets correction at quantum level. Universally, these corrections are logarithmic and exponential in nature. We analyze the impacts of these quantum corrections on thermodynamics of Born-Infeld BTZ black hole in massive gravity by considering both such kinds of correction. We do comparative analysis of corrected thermodynamics with their equilibrium values. Here, we find that the exponential correction yields to the second point of the first order phase transition. Also, quantum correction effects significantly on the Helmholtz free energy of larger black holes. We study the equation of state for the exponential corrected black hole to obtain a leading order virial expansion.