Unruh entropy of Schwarzschild black hole

TL;DR

This paper estimates the entropy generated by Unruh radiation around a Schwarzschild black hole, comparing it to the black hole's entropy, and finds a quantum number-dependent ratio that varies significantly with particle spin.

Contribution

It provides an analytical estimate of Unruh entropy for Schwarzschild black holes, incorporating particle spin and mass dependence, extending understanding of black hole entropy contributions.

Findings

Unruh entropy ratio varies from 0% to 19% depending on particle spin.

The ratio is highly sensitive to quantum numbers for large black holes.

The method can be extended to other degrees of freedom of emitted particles.

Abstract

The entropy produced by the Unruh radiation is estimated and compared to the entropy of a Schwarzschild black hole. We simulate a spherical system of mass $ M $ by set of Unruh horizons and estimate the total entropy of the outgoing radiation. Dependence on mass and spin of the emitted particles is taken into account. The obtained results can be easily extended to any other intrinsic degrees of freedom of outgoing particles. The ratio of Unruh entropy to the Schwarzschild black hole entropy is derived in exact analytical form. For large black holes this ratio is highly sensitive to quantum numbers of emitted quanta, e.g., spin $ s $, for which it varies from $ 0\% $ for $ s = 0 $ to $ 19\% $ for $ s = 5/2 $.