Thermodynamic structure of field equations near apparent horizon for radiating black holes

TL;DR

This paper explores the thermodynamic interpretation of Einstein's equations near the apparent horizon of radiating black holes, establishing an analogy with thermodynamic identities in both four and higher dimensions.

Contribution

It demonstrates that Einstein's field equations near the apparent horizon can be expressed as a thermodynamic identity for nonstationary radiating black holes in various dimensions.

Findings

Einstein equations near the horizon resemble thermodynamic identities

The thermodynamic analogy holds in both four and higher dimensions

Kinematical parameters are defined via null vectors

Abstract

We study the intriguing analogy between gravitational dynamics of the horizon and thermodynamics for the case of nonstationary radiating spherically symmetric black holes both in four dimensions and higher dimensions. By defining all kinematical parameters of nonstationary radiating black holes in terms of null vectors, we demonstrate that it is possible to interpret the Einstein field equations near the apparent horizon in the form of a thermodynamical identity $TdS=dE+PdV$.