https://doi.org/10.1140/epjp/s13360-023-03938-x
Regular Article
Geodesics in geometrothermodynamics (GTD) type II geometry of 4D asymptotically anti-de-Sitter black holes
1
Department of Physics, Dibrugarh University, 786004, Dibrugarh, Assam, India
2
Physics Group, Bhabha Atomic Research Center, 400085, Mumbai, Maharashtra, India
Received:
20
December
2022
Accepted:
28
March
2023
Published online:
19
April
2023
In this work, we study the thermodynamic geodesics of 4D asymptotically anti-de Sitter black holes in the context of the geometrothermodynamics (GTD) type II metric. We construct GTD type II metrics for four different black holes: 4D Kerr–Newman AdS (KN-AdS), Kerr-AdS (K-AdS), Reissner–Nordstrom AdS (RN-AdS), and Dyonic AdS black holes in various ensembles. For K-AdS and RN-AdS black holes, we work in canonical as well as grand canonical ensembles. For KN-AdS and Dyonic AdS black holes, in addition to these two ensembles, we also consider a fixed charged ensemble. For each case, we solve the corresponding geodesic equations numerically and analyze their behavior near the spinodal curves. These spinodal curves, which separate the positive specific heat region from the negative specific heat region, can be treated as the boundary between two black hole phases in the thermodynamic parameter space. The points on the spinodal curve are the points in parameter space at which we reach Davies’ temperature. We find that the geodesics, in all the cases under consideration, are confined to a single phase and exhibit either turning behavior or incompleteness near the spinodal curve (Davies’ temperature). This is universally true for GTD type II geodesics in KN-AdS, K-AdS, RN-AdS, and Dyonic AdS black holes in different ensembles. From this, we conclude that the turning behavior or incompleteness of geodesics in GTD type II geometry can be used as an indicator of phase transitions in 4D asymptotically AdS black holes.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
