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Thermal instability and thermodynamic geometry of topological dilaton black holes coupled to nonlinear electrodynamics

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Abstract

We study topological dilaton black holes of Einstein gravity in the presence of exponential nonlinear electrodynamics. The event horizons of these black holes can be a two-dimensional positive, zero or negative constant curvature surface. We analyze thermodynamics of these solutions by calculating all conserved and thermodynamic quantities and showing that the first law holds on the black hole horizon. Then, we perform the stability analysis in both canonical and grand canonical ensemble and disclose the effects of the dilaton and nonlinear electrodynamics on the thermal stability of the solutions. Finally, we study the phase transition points of these black holes in the thermodynamic geometry approach.

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Acknowledgments

A. Sheykhi thanks Shiraz University Research Council. This work has been supported financially by 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, 71454, Shiraz, Iran

    A. Sheykhi & S. Hajkhalili

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

    A. Sheykhi

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  1. A. Sheykhi
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  2. S. Hajkhalili
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Correspondence to A. Sheykhi.

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Sheykhi, A., Hajkhalili, S. Thermal instability and thermodynamic geometry of topological dilaton black holes coupled to nonlinear electrodynamics. Gen Relativ Gravit 47, 135 (2015). https://doi.org/10.1007/s10714-015-1984-3

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  • DOI: https://doi.org/10.1007/s10714-015-1984-3

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