Black Hole Entropy from Entropy of Hawking Radiation

TL;DR

This paper presents a straightforward method to determine a black hole's entropy by relating it to the entropy of its Hawking radiation, providing a new perspective on black hole thermodynamics.

Contribution

It introduces a simple relation between the entropy loss of a black hole and the entropy of emitted Hawking radiation, enabling direct calculation of black hole entropy from radiation data.

Findings

The entropy loss of a black hole is 3/4 of the entropy of emitted radiation.

The method allows calculating the Bekenstein-Hawking entropy from Hawking radiation.

The approach simplifies understanding black hole evaporation and entropy relations.

Abstract

We provide a simple way for calculating the entropy of a Schwarzschild black hole from the entropy of its Hawking radiation. To this end, we show that if a thermodynamic system loses its energy only through the black body radiation, its loss of entropy is always 3/4 of the entropy of the emitted radiation. This proposition enables us to relate the entropy of an evaporating black hole to the entropy of its Hawking radiation. Explicitly, by calculating the entropy of the Hawking radiation emitted in the full period of evaporation of the black hole, we find the Bekenstein-Hawking entropy of the initial black hole.