Page curve and phase transition in deformed Jackiw-Teitelboim gravity

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.

Automated summary

We study the behavior of the Page curve and the island paradigm for a deformed Jackiw-Teitelboim black hole with the presence of a phase transition. The black hole exhibits a van der Waals-Maxwell-like phase structure due to its coupling with a Maxwell field. We investigate different situations with different charges in the fixed charge ensemble, which affect the system's phase structure. The Page curve exists only in the presence of charges, with a van der Waals-Maxwell-like phase transition resulting in three black hole solutions.