Abstract
The thermodynamics of the Reissner–Nordström black hole at the charge-to-mass ratio of \(\sqrt{3}/2\) is studied. We show that there exists infinite discontinuity not only in the heat capacity but also in the electromagnetic potential and hence in the Gibbs free energy. Despite the existence of an infinite discontinuity in the heat capacity, it is shown that there exists no phase transition in the Reissner–Nordström black hole. The discontinuity may be merely an artefact of the change in the slope of the |Q| vs. M curve when the charge-to-mass ratio crosses \(\sqrt{3}/2\) . This may signify that the horizon temperature is not a well-behaved thermodynamic parameter in the black hole thermodynamics.
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Ablu Meitei, I., Yugindro Singh, K., Ibungochouba Singh, T. et al. Phase transition in the Reissner–Nordström black hole. Astrophys Space Sci 327, 67–69 (2010). https://doi.org/10.1007/s10509-010-0271-8
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DOI: https://doi.org/10.1007/s10509-010-0271-8