Failure of Standard Thermodynamics in Planck Scale Black Hole System

TL;DR

This paper investigates the thermodynamics of Planck scale black holes using noncommutative geometry and the generalized uncertainty principle, revealing unusual behavior that suggests the need for a new thermodynamic framework.

Contribution

It compares noncommutative geometry and GUP approaches to black hole evaporation, highlighting their relation and the breakdown of standard thermodynamics at the Planck scale.

Findings

Unusual thermodynamic behavior observed in Planck size black hole evaporation

Standard thermodynamics fails at the Planck scale

Potential need for fractal nonextensive thermodynamics

Abstract

The final stage of the black hole evaporation is a matter of debates in the existing literature. In this paper, we consider this problem within two alternative approaches: noncommutative geometry(NCG) and the generalized uncertainty principle(GUP). We compare the results of two scenarios to find a relation between parameters of these approaches. Our results show some extraordinary thermodynamical behavior for Planck size black hole evaporation. These extraordinary behavior may reflect the need for a fractal nonextensive thermodynamics for Planck size black hole evaporation process.