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Thermodynamic Geometry and Critical Behavior of Black Holes

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arxiv gr-qc/0512035 v1 pith:ZEYHATTL submitted 2005-12-06 gr-qc hep-th

Jianyong Shen , Rong-Gen Cai , Bin Wang , Ru-Keng Su This is my paper · ORCID
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keywords blackholesgeometryrn-adsbehaviorcriticalholekerr
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abstract

Based on the observations that there exists an analogy between the Reissner-Nordstr\"om-anti-de Sitter (RN-AdS) black holes and the van der Waals-Maxwell liquid-gas system, in which a correspondence of variables is $(\phi, q) \leftrightarrow (V,P)$, we study the Ruppeiner geometry, defined as Hessian matrix of black hole entropy with respect to the internal energy (not the mass) of black hole and electric potential (angular velocity), for the RN, Kerr and RN-AdS black holes. It is found that the geometry is curved and the scalar curvature goes to negative infinity at the Davies' phase transition point for the RN and Kerr black holes. Our result for the RN-AdS black holes is also in good agreement with the one about phase transition and its critical behavior in the literature.

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Cited by 2 Pith papers

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  1. Quantum-Corrected Thermodynamics and Phase Structure of AdS Euler-Heisenberg Black Hole

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    Thermal fluctuation corrections to entropy change the stability and phase structure of an AdS Euler-Heisenberg black hole, producing multiple specific-heat divergences and a stable small-hole phase.

  2. Thermodynamic Curvature and Topological Insights of Hayward Black Holes with String Fluids

    gr-qc 2025-06 reject novelty 4.0 of 10

    For Hayward-AdS black holes with string fluids, the normalized thermodynamic curvature is mostly negative but becomes repulsive for high charge at small volume, and the total topological charge is W=0 for epsilon=-1 a...

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