Generalized free energy landscape of black hole phase transition

Abstract

Recently, the stochastic dynamical model based on the free energy landscape was proposed to quantify the kinetics of the black hole phase transition. An essential concept is the generalized free energy of the fluctuating black hole, which was defined in terms of the thermodynamic relation previously. In this work, by employing the Gibbons-Hawking path integral approach to black hole thermodynamics, we show that the generalized free energy can be derived from the Einstein-Hilbert action of the Euclidean gravitational instanton with the conical singularity. This work provides a concrete and solid foundation for the free energy landscape formalism of black hole phase transition.

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• Revisiting thermodynamic topologies of black holes
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• Topological classes of thermodynamics of the four-dimensional static accelerating black holes
• The topological natures of the Gauss-Bonnet black hole in AdS space
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• Universal thermodynamic topological classes of rotating black holes
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• Black Hole Chemistry: the first 15 years
• Topology of the landscape and dominant kinetic path for the thermodynamic phase transition of the charged Gauss-Bonnet AdS black holes
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• Thermodynamic topological classes of the rotating, accelerating black holes
• Universal thermodynamic topological classes of three-dimensional BTZ black holes
• Recovery of consistency in thermodynamics of regular black holes in Einstein's gravity coupled with nonlinear electrodynamics
• ${\tilde{W}}^{1+}$ subclass: Extending the topological classification of black hole thermodynamics
• Thermodynamic phase transition and winding number for the third-order Lovelock black hole
• Black hole thermodynamics from an ensemble-averaged theory
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• Born-Infeld-AdS black hole phase structure: Landau theory and free energy landscape approaches
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• Differential topology and micro-structure of black hole in Einstein-Euler-Heisenberg spacetimes with exponential entropy
• Dimensional structure of thermodynamic topology in ultraspinning Kerr-AdS black holes
• Out-of-Time-Order-Correlation in perturbed quantum wells