Gravitational attraction is presented as the gradient of a negative entropy deficit, equal to the red-shifted shell energy divided by Hawking temperature, applied to a black hole with a static thin shell.
Generalized free energy landscape of black hole phase transition
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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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Holographic Ordering and Negative entropy in Non-equilibrium Euclidean Black Hole Path Integralsl
Gravitational attraction is presented as the gradient of a negative entropy deficit, equal to the red-shifted shell energy divided by Hawking temperature, applied to a black hole with a static thin shell.