Thermodynamic stability of charged BTZ black holes: Ensemble dependency problem and its solution

TL;DR

This paper addresses the ensemble dependency problem in the thermodynamic stability analysis of charged BTZ black holes and proposes a solution by treating the cosmological constant as a thermodynamic variable, ensuring consistent stability conditions across ensembles.

Contribution

It introduces a method to eliminate ensemble dependency in black hole thermodynamics by incorporating the cosmological constant as a variable, applicable to both linear and nonlinear electrodynamics.

Findings

Ensemble dependency is resolved by including the cosmological constant as a thermodynamic variable.

Thermal stability conditions become consistent across different ensembles.

Nonlinear electrodynamics modifies the black hole's geometric and thermodynamic behavior.

Abstract

Motivated by the wide applications of thermal stability and phase transition, we investigate thermodynamic properties of charged BTZ black holes. We apply the standard method to calculate the heat capacity and the Hessian matrix and find that thermal stability of charged BTZ solutions depends on the choice of ensemble. To overcome this problem, we take into account cosmological constant as a thermodynamical variable. By this modification, we show that the ensemble dependency is eliminated and thermal stability conditions are the same in both ensembles. Then, we generalize our solutions to the case of nonlinear electrodynamics. We show how nonlinear matter field modifies the geometrical behavior of the metric function. We also study phase transition and thermal stability of these black holes in context of both canonical and grand canonical ensembles. We show that by considering the cosmological constant as a thermodynamical variable and modifying the Hessian matrix, the ensemble dependency of thermal stability will be eliminated.