Nonequilibrium Black Hole Thermodynamics in Anti-de Sitter Spacetime

Kai Lin,Luciano Petruzziello

doi:10.1155/2021/4613870

Abstract

This work discusses the black hole thermodynamics in a weak dynamical Anti-de Sitter spacetime, which should be described by the nonequilibrium thermodynamics, because the metric depends on the time coordinate. Taking the Vaidya-Anti-de Sitter black hole spacetime as an example, the local entropy balance equations and principle of minimum entropy generation are derived, and finally, some irreversible effects in nonequilibrium thermodynamics are studied by using the Onsager reciprocal relation.

Highlights

In 1975, by using the quantum field theory in curved spacetime, Hawking proposed that a black hole could produce radiation at horizon [1, 2], and the effect is named as Hawking radiation, which implies a profound relation among gravitational theory, quantum theory, and thermodynamics
The physical phenomena in the linear region can be well described by modern nonequilibrium thermodynamics, and we believe that the linear region corresponds to the black hole thermodynamics of a weak dynamical black hole, which means the timedependent part is far smaller than the stationary part of this black hole metric, so that several physical effects could be investigated by expanding the perturbation near the equilibrium state and the Onsager reciprocal relation
Speaking of the principle of extremum entropy generation, we find there is a critical value λc, and the principle of minimum entropy generation is satisfied as λ < λc, but the entropy production rate becomes a monotone increasing function when λ > λc

Summary

Introduction

In 1975, by using the quantum field theory in curved spacetime, Hawking proposed that a black hole could produce radiation at horizon [1, 2], and the effect is named as Hawking radiation, which implies a profound relation among gravitational theory, quantum theory, and thermodynamics. The fact implies that a dynamical black hole should satisfy nonequilibrium thermodynamics, which includes many dynamical irreversible processes, such as the electrodynamical effect, thermodynamical effect, and transfer phenomenon. These effects can give a good explanation for the actual phenomena of life. The physical phenomena in the linear region can be well described by modern nonequilibrium thermodynamics, and we believe that the linear region corresponds to the black hole thermodynamics of a weak dynamical black hole, which means the timedependent part is far smaller than the stationary part of this black hole metric, so that several physical effects could be investigated by expanding the perturbation near the equilibrium state and the Onsager reciprocal relation.

The Balance Relation of Local Entropy in Weak Dynamical Black Hole Spacetime

Irreversible Dynamical Effect in Linear Region

Conclusion