Black Hole Evaporation and Nonequilibrium Thermodynamics for a Radiation Field

TL;DR

This paper develops a nonequilibrium thermodynamic framework for analyzing black hole evaporation in empty space, focusing on the entropy evolution of the Hawking radiation field.

Contribution

It introduces a nonequilibrium thermodynamics approach for radiation fields and applies it to model black hole evaporation, providing insights into entropy dynamics.

Findings

Entropy increases over time during evaporation

Hawking radiation remains in a nonequilibrium state

The model predicts the entropy evolution of the radiation field

Abstract

When a black hole is put in an "empty" space (zero temperature space) on which there is no matter except the matter of the Hawking radiation (Hawking field), then an outgoing energy flow from the black hole into the empty space exists. By the way, an equilibrium between two arbitrary systems can not allow the existence of an energy (heat) flow from one system to another. Consequently, in the case of a black hole evaporation in the empty space, the Hawking field should be in a nonequilibrium state. Hence the total behaviour of the evaporation, for example the time evolution of the total entropy, should be analysed with a nonequilibrium thermodynamics for the Hawking field. This manuscript explains briefly the way of constructing a nonequilibrium thermodynamic theory for a radiation field, and apply it to a simplified model of a black hole evaporation to calculate the time evolution of the total entropy.