The spectrum of Hawking radiation in Tsallis statistical mechanics

TL;DR

This paper explores how Hawking radiation spectra are altered when analyzed through Tsallis statistical mechanics instead of traditional Boltzmann-Gibbs, revealing modifications to black hole radiation laws and effective radii.

Contribution

It introduces a framework for calculating Hawking radiation spectra using Tsallis statistics, extending the understanding beyond standard thermodynamics.

Findings

Modified Stefan-Boltzmann law derived

Altered power of Hawking radiation calculated

Black hole lifetime and large q effects discussed

Abstract

Hawking radiation is one of the cores in modern gratitational theory. Several articles have calculated the spectrum of Hawking radiation in Boltzmann-Gibbs statistical mechanics. However, based on recent researches, gravitational systems cannot be studied by the standard statistical mechanics. In this article, we calculate the modification to the spectrum of Hawking radiation in Tsallis statistical mechanics. We obtain the modified Stefan-Boltzmann's law and modified power of Hawking radiation. We confirm the conclusion proposed by Giddings, namely, the radiation should originate from the effective radius, which extends well outside the horizon of black-hole. The lifetime of black hole and the effect of large q are discussed as well.