Generalized uncertainty principle and black hole thermodynamics

TL;DR

This paper investigates black hole thermodynamics under the generalized uncertainty principle, deriving exact relations for mass, temperature, entropy, and critical masses for Schwarzschild and Reissner-Nordström black holes, revealing quantum corrections to classical results.

Contribution

It provides exact expressions for black hole thermodynamics incorporating GUP corrections, including higher-order effects on entropy and horizon area relations.

Findings

Critical and remnant masses are larger than the singular mass.

Entropy obeys the area theorem with GUP corrections.

Higher-order GUP corrections modify the horizon area relations.

Abstract

We study the Schwarzschild and Reissner-Nordstr\"{o}m black hole thermodynamics using the simplest form of the generalized uncertainty principle (GUP) proposed in the literature. The expressions for the mass-temperature relation, heat capacity and entropy are obtained in both cases from which the critical and remnant masses are computed. Our results are exact and reveal that these masses are identical and larger than the so called singular mass for which the thermodynamics quantities become ill-defined. The expression for the entropy reveals the well known area theorem in terms of the horizon area in both cases upto leading order corrections from GUP. The area theorem written in terms of a new variable which can be interpreted as the reduced horizon area arises only when the computation is carried out to the next higher order correction from GUP.