Dynamic black-hole entropy

TL;DR

This paper explores two non-statistical definitions of entropy for dynamic black holes, demonstrating their equivalence and deriving the entropy as one-quarter of the trapping horizon area in Einstein gravity.

Contribution

It introduces and compares two non-statistical entropy definitions for dynamic black holes, adapting Wald's method with the Kodama flow.

Findings

Both definitions agree for Einstein gravity.

Entropy equals one-quarter of the trapping horizon area.

The first law relates energy supply to surface gravity and differential.

Abstract

We consider two non-statistical definitions of entropy for dynamic (non-stationary) black holes in spherical symmetry. The first is analogous to the original Clausius definition of thermodynamic entropy: there is a first law containing an energy-supply term which equals surface gravity times a total differential. The second is Wald's Noether-charge method, adapted to dynamic black holes by using the Kodama flow. Both definitions give the same answer for Einstein gravity: one-quarter the area of the trapping horizon.