The Effect of R\'enyi Entropy on Hawking Radiation

TL;DR

This paper investigates how Rényi entropy influences Hawking radiation, suggesting that for small effects, radiation originates from a quantum atmosphere beyond the horizon, aligning with Giddings' hypothesis, especially in finite dimensions.

Contribution

It introduces the consideration of Rényi entropy effects on Hawking radiation power, extending previous models and analyzing implications for different dimensional scenarios.

Findings

Small Rényi entropy effects support the quantum atmosphere origin of Hawking radiation.

In infinite dimensions, both horizon and atmosphere origins are equally plausible.

Large Rényi entropy effects can significantly alter the radiation power spectral density.

Abstract

It is widely believed that Hawking radiation originates from excitations near the horizons of black holes. However, Giddings proposed that the Hawking radiation spectrum that characterizes evaporating semi-classical black holes originates from a quantum atmosphere, which extends beyond the horizon of a black hole. Although several research projects have been conducted in this field, they have not yet taken into account the effect of R\'enyi entropy. In the present article, we will therefore consider the effect of R\'enyi entropy on Hawking radiation power. We assume that if the effect of R\'enyi entropy is very small, we suggest that the Hawking radiation should originate from the quantum atmosphere which extends beyond the black hole's horizon for finite dimensions. That is, that Giddings' suggestion is the more likely of the above possibilities. However, for infinite dimensions, both suggestions are equally credible. We briefly consider the very large effect of R\'enyi entropy on Hawking radiation power as well. We find that if the effect of R\'enyi entropy is very large and {\omega}/T_{BH} is very small, then the power spectral density S_R is proportional to the power spectral density S_{BH}.