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

Understand

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.