Statistical approaches and the Bekenstein bound conjecture in Schwarzschild black holes

TL;DR

This paper investigates the relationship between geometric and thermodynamic properties of black holes, examining how different non-Gaussian entropy measures affect the validity of the Bekenstein bound in Schwarzschild black holes.

Contribution

It introduces the use of non-Gaussian entropies like Barrow, Tsallis, and Kaniadakis to analyze black hole entropy, revealing potential limitations of the Bekenstein bound.

Findings

Bekenstein-Hawking entropy satisfies the bound

Non-Gaussian entropies may violate the bound

Results suggest new perspectives on black hole thermodynamics

Abstract

One of the challenges of today's theoretical physics is to fully understand the connection between a geometrical object like area and a thermostatistical one like entropy, since area behaves analogously like entropy. The Bekenstein bound suggests a universal constraint for the entropy of a region in a flat space. The Bekenstein-Hawking entropy of black holes satisfies the Bekenstein bound conjecture. In this paper we have shown that when we use important non-Gaussian entropies, like the ones of Barrow, Tsallis and Kaniadakis in order to describe the Schwarzschild black hole, then the Bekenstein bound conjecture seems to fail.