Thermodynamic phase transition based on the non-singular temperature

TL;DR

This paper introduces a non-singular temperature model for black holes that remains finite during evaporation, enabling the study of phase transitions and stability of small and large black holes.

Contribution

A novel non-singular temperature function is constructed, allowing consistent thermodynamic analysis of black hole evaporation and phase transitions.

Findings

Small black holes can be stable below a certain temperature.

Hot flat space is metastable and decays into stable black holes.

The temperature remains finite during black hole evaporation.

Abstract

The Hawking temperature for the Schwarzschild black hole is divergent when the mass of the black hole vanishes; however the corresponding geometry becomes the Minkowski spacetime whose intrinsic temperature is zero. In connection with this issue, we construct a non-singular temperature which follows the Hawking temperature for the large black hole while it vanishes when the black hole completely evaporated. In order for thermodynamic significances of this modified temperature, we calculate thermodynamic quantities and study phase transitions. It turns out that even the small black hole can be stable below a certain temperature, and the hot flat space is always metastable so that it decays into the stable small black hole or the stable large black hole.