Nonextensive Black Hole Entropy and Quantum Gravity Effects at the Last Stages of Evaporation

TL;DR

This paper explores how quantum gravity effects, modeled by the Generalized Uncertainty Principle, influence black hole entropy and temperature, revealing finite end-stage values and modifications to radiation sparsity during evaporation.

Contribution

It introduces GUP effects into nonextensive black hole thermodynamics using Rényi entropy, showing finite entropy and temperature at evaporation's end and analyzing radiation sparsity modifications.

Findings

Black hole entropy and temperature become finite at the end of evaporation.

GUP effects modify the sparsity of Hawking radiation.

Comparison between Rényi and Hawking radiation sparsity.

Abstract

We analyze the Generalized Uncertainty Principle (GUP) impact onto the nonextensive black hole thermodynamics by using R\'enyi entropy. We show that when introducing GUP effects, both R\'enyi entropy and temperature associated to black holes have finite values at the end of the evaporation process. We also study the sparsity of the radiation, associated with R\'enyi temperature, and compare it with the sparsity of Hawking radiation. Finally, we investigate GUP modifications to the sparsity of the radiation when GUP effects are introduced into R\'enyi temperature.