Black hole thermodynamics with generalized uncertainty principle

TL;DR

This paper investigates how the generalized uncertainty principle affects small black hole thermodynamics, revealing that minimal length prevents certain phase transitions and exploring the possibility of black hole remnants in a cavity.

Contribution

It introduces the impact of the GUP on black hole thermodynamics, highlighting the role of minimal length in phase transition suppression and analyzing black hole remnants.

Findings

Minimal length from GUP interrupts phase transition for small black holes.

Black hole remnants do not transition to large black holes in a cavity.

GUP modifies the thermodynamic behavior of small black holes.

Abstract

We apply the generalized uncertainty principle to the thermodynamics of a small black hole. Here we have a black hole system with the UV cutoff. It is shown that the minimal length induced by the GUP interrupts the Gross-Perry-Yaffe phase transition for a small black hole. In order to see whether the black hole remnant takes place a transition to a large black hole, we introduce a black hole in a cavity (IR system). However, we fail to show the phase transition of the remnant to the large black hole.