Page Curve and Phase Transition in deformed Jackiw-Teitelboim Gravity

TL;DR

This paper investigates the entanglement entropy and Page curve behavior of deformed Jackiw-Teitelboim black holes with phase transitions, revealing how charge influences black hole phases and the existence of the Page curve.

Contribution

It demonstrates the impact of phase transitions and charge on the Page curve and entanglement islands in deformed JT gravity, highlighting new phase-dependent behaviors.

Findings

Page curve exists only in certain charged black hole phases

Extremal black hole Page time approaches zero during phase transition

Unstable small black hole does not exhibit a Page curve

Abstract

We consider the entanglement island in a deformed Jackiw-Teitelboim black hole in the presence of the phase transition. This black hole has the van der Waals-Maxwell-like phase structure as it is coupled with a Maxwell field. We study the behavior of the Page curve of this black hole by using the island paradigm. In the fixed charge ensemble, we discuss different situations with different charges that influence the system's phase structure. There is only a Hawking-Page phase transition in the absence of charges, which leads to an unstable small black hole. Hence, the related Page curve does not exist. However, a van der Waals-Maxwell-like phase transition occurs in the presence of charges. This yields three black hole solutions. The Page curve of the middle size black hole does not exist. For the extremal black hole, the Page time approaches zero in the phase transition situation but becomes divergent without the phase transition. In a word, we study the Page curve and the island paradigm for different black hole phases and in different phase transition situations.