On superstatistics and black hole quasinormal modes

TL;DR

This paper explores how non-extensive superstatistics-based entropies influence the minimum spin of black holes, revealing dependencies on area and parameters, especially affecting micro black holes.

Contribution

It introduces a method to determine the minimum black hole spin using non-extensive entropies derived from superstatistics, extending previous Boltzmann-Gibbs-based results.

Findings

$j_{min}$ depends on black hole area and non-extensive parameters

Modification affects only micro black holes, not classical ones

Results align with Boltzmann-Gibbs statistics for classical black holes

Abstract

It is known that using Boltzmann-Gibbs statistics, Bekenstein-Hawking entropy $S_{HB}$, and the quasinormal modes of black holes, one finds that the lowest value of spin is $j_{min}=1$. In this paper, we determine $j_{min}$, using non-extensive entropies that depend only on the probability (known as Obregon's entropies and have been derived from superstatistics). We also calculate $j_{min}$ for a set of non-extensive entropies that have free parameters and are written in terms of $S_{BH}$. We find that $j_{min}$ depends on the area and the non-extensive parameter. For the non-extensive entropies that only depend on the probability, we find that the modification is only present for micro black holes. For classical black holes the results are the same as for the Boltzmann-Gibbs statistics.