Two critical phenomena in the exactly soluble quantized Schwarzschild black hole

TL;DR

This paper investigates thermodynamic phase transitions of Schwarzschild black holes considering quantum back reaction effects, revealing an additional phase transition and stability properties influenced by conformal anomalies.

Contribution

It introduces an analysis of phase transitions including conformal anomaly effects, identifying a new phase transition and stability characteristics of small and large black holes.

Findings

Existence of an additional phase transition beyond Hawking-Page.

Small black holes are more probable than hot flat space above a second critical temperature.

Unstable small black holes decay into stable large black holes due to thermodynamic stability.

Abstract

We study thermodynamic quantities and phase transitions of a spherically symmetric Schwarzschild black hole by taking into account the back reaction through the conformal anomaly of matter fields, and show that there exists an additional phase transition to the conventional Hawking-Page phase transition. The small black hole is more probable than the hot flat space above a second critical temperature, while it is less probable than the hot flat space in the classical Schwarzschild black hole. However, the unstable small black hole eventually should decay into the stable large black hole because the conformal anomaly does not change its thermodynamic stability.