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Thermodynamics of Ayón-Beato–García–AdS black holes in 4D Einstein–Gauss–Bonnet gravity

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Abstract

Within a family of Ayón-Beato–García black holes in four-dimensional Einstein–Gauss–Bonnet (EGB) gravity in Anti-de Sitter space-time geometries, we study various thermodynamical aspects by computing the relevant quantities which include the mass, the Hawking temperature, the entropy, the heat capacity, and the Gibbs free energy. We find that the heat capacity is discontinuous at critical values of the radial coordinate, with sign changes that hint at transitions between small and large black holes near such critical values. After providing evidence that such solutions exhibit a P–v criticality, we analyze the Gibbs free energy and show that it shares similarities with the Van der Waals phase transitions. In order to confirm the second-order nature of the phase transition points, we study the thermodynamical curvature of the Ruppeiner metric, finding that the singular points of such a curvature coincide with the ones at which the heat capacity diverges.

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Notes

  1. We recall that the generalized moduli space gives rise to an extended entropy expression going beyond the Bekenstein–Hawking entropy-area relation (namely, \(S=A/4\), where \(A=4\pi r_{+}^{2}\)) [26].

  2. By taking \(q=0\), one can recover the pressure

    $$\begin{aligned} P=\frac{T(r_{+}^{2}+\alpha )}{2r_{+}^{3}}-\frac{r_{+}^{2}-\alpha }{8\pi r_{+}^{4}}. \end{aligned}$$
    (4.3)

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Acknowledgements

AB would like to thank A. Belfakir, H. Belmahi, M. Benali, H. El Moumni, R. Harzallah, Y. Hassouni, A. Lowe, A. Marrani, P. Meessen, and M. B. Sedra for discussions, collaborations, and scientific help. YS would like to thank D. V. Singh for email discussions on related subjects. The authors would like also to thank the editor and the anonymous referee for interesting comments and suggestions. This work is partially supported by the ICTP through AF.

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  1. Département de physique, Équipe des Sciences de la matière et du rayonnement, ESMaR Faculté des Sciences, Université Mohammed V de Rabat, Rabat, Morocco

    A. Belhaj & Y. Sekhmani

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Correspondence to A. Belhaj.

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Belhaj, A., Sekhmani, Y. Thermodynamics of Ayón-Beato–García–AdS black holes in 4D Einstein–Gauss–Bonnet gravity. Eur. Phys. J. Plus 137, 278 (2022). https://doi.org/10.1140/epjp/s13360-022-02495-z

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