Topology of critical points and Hawking-Page transition

Abstract

Using the Bragg-Williams construction of an off-shell free energy we compute the topological charge of the Hawking-Page transition point for black holes in AdS. A computation following from a related off-shell effective potential in the boundary gauge dual matches the value of topological charge obtained in the bulk. We also compute the topological charges of the equilibrium phases of these systems, which follow from the saddle points of the appropriate free energy. The locally stable and unstable phases turn out to have topological charges opposite to each other, with the total being zero, in agreement with the result obtained from a related construction [arXiv:2208.01932].

14 pages, 6 figures

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• Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume
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Cited by in corpus (4)

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• Thermodynamic topology of black Holes in f(R) gravity
• Topological classes of thermodynamics of black holes in perfect fluid dark matter background
• Generalized free energy and dynamical state transition of the dyonic AdS black hole in the grand canonical ensemble