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

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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.

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Acknowledgments

We would like to thank the anonymous referee for valuable suggestions. We also acknowledge A. Poostforush for reading the manuscript. We wish to thank the Shiraz University Research Council. This work has been supported financially by the Research Institute for Astronomy and Astrophysics of Maragha, Iran.

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Authors and Affiliations

  1. Physics Department and Biruni Observatory, College of Sciences, Shiraz University, Shiraz, 71454, Iran

    S. H. Hendi, S. Panahiyan & R. Mamasani

  2. Research Institute for Astrophysics and Astronomy of Maragha (RIAAM), P.O. Box 55134-441, Maragha, Iran

    S. H. Hendi

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  1. S. H. Hendi
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Correspondence to S. H. Hendi.

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Hendi, S.H., Panahiyan, S. & Mamasani, R. Thermodynamic stability of charged BTZ black holes: ensemble dependency problem and its solution. Gen Relativ Gravit 47, 91 (2015). https://doi.org/10.1007/s10714-015-1932-2

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