Hawking-Page phase transition, Page curve and islands in black holes

TL;DR

This paper investigates how Hawking-Page phase transitions influence the Page curve and information release in evaporating BTZ black holes, revealing phase-dependent behaviors and a potential universal escape mechanism.

Contribution

It introduces the impact of Hawking-Page phase transitions on black hole information dynamics, including phase-dependent information release and the role of islands.

Findings

Phase transition can occur before, at, or after the Page time.

Information release can happen without islands if the transition occurs before the Page time.

A first-order phase transition can cause all black hole information to be released at once.

Abstract

We study the Page curve and the effect of the Hawking-Page phase transition in the Vaidya model of evaporating BTZ black holes, both with and without islands. The phase transition can occur before, at, or after the Page time. When it occurs before the Page time, the information release does not require an island yet still reproduces the Page curve. From the first law of entanglement, the entanglement temperature changes from negative to positive, diverging at the Page time. Thus, the information deposition phase corresponds to a negative temperature, and the release phase to a positive temperature. If the Hawking-Page phase transition takes place, all black hole information is released at once via a quantum jump. We speculate that first-order phase transitions universally affect black hole information, providing an alternative escape mechanism independent of Hawking radiation.