Thermodynamics of dynamical black holes beyond perturbation theory

TL;DR

This paper extends black hole thermodynamics to dynamical, non-equilibrium situations using quasi-local horizons, establishing a new first law and a quantitative second law based on horizon fluxes.

Contribution

It introduces a generalized thermodynamic framework for dynamical black holes using quasi-local horizons, moving beyond perturbative and event horizon limitations.

Findings

New first law applies to arbitrarily far from equilibrium black holes.

Second law relates area change to energy fluxes at the horizon.

Entropy is identified with the area of marginally trapped surfaces.

Abstract

The close similarities of the three laws of black hole mechanics, discovered by Bardeen, Carter and Hawking, with the laws of thermodynamics led to the identification of a multiple of the area of the event horizon with entropy. However, developments over the past two decades have shown that this paradigm has some important limitations, especially because of the teleological nature of event horizons. After a brief review of these limitations, we will show that they can be overcome using quasi-local horizons. Specifically, the new first law applies to black holes in general relativity that can be \emph{arbitrarily far from equilibrium} and refers to \emph{finite} changes that occur due to \emph{physical processes} at the horizon. The second law is now a \emph{quantitative} statement that relates the change in the area of a dynamical horizon segment due to fluxes of energy falling into the black hole. Together, they lead one to identify black hole entropy with the area of marginally trapped surfaces in quasi-local horizons, generalizing recent {perturbative} findings that it should be identified not with the area of the event horizon but with the area of a marginally trapped surface inside it.