Thermodynamics of a black hole based on a generalized uncertainty principle

TL;DR

This paper investigates black hole thermodynamics within a cavity using a generalized uncertainty principle, revealing how quantum effects influence stability, entropy, and phase transitions of black holes.

Contribution

It introduces a symmetric generalized uncertainty relation into black hole thermodynamics, analyzing its impact on stability and phase behavior of black holes in a cavity.

Findings

Small black holes are unstable and may decay into minimal or large black holes.

The generalized uncertainty parameters affect thermodynamic quantities like energy and entropy.

Constraints are discussed for large black holes relative to the cavity size.

Abstract

We study thermodynamic quantities and the stability of a black hole in a cavity using the Euclidean action formalism by Gibbons and Hawking based on the generalized uncertainty relation which is extended in a symmetric way with respect to the space and momentum without loss of generality. Two parameters in the uncertainty relation affect the thermodynamical quantities such as energy, entropy, and the heat capacity. In particular, it can be shown that the small black hole is unstable and it may decay either into a minimal black hole or a large black hole. We discuss a constraint for a large black hole comparable to the size of the cavity in connection with the critical mass.