Page curve from dynamical branes in JT gravity

TL;DR

This paper models black hole evaporation using JT gravity with dynamical FZZT branes, showing the entanglement entropy reproduces the Page curve and analyzing phase transitions and late-time behavior.

Contribution

It introduces a dynamical brane model in JT gravity that captures the Page curve and phase transition phenomena in black hole evaporation.

Findings

Entropy initially increases then decreases, matching the Page curve.

System undergoes a phase transition at the end of evaporation.

Late-time entropy decreases monotonically, supported by analytical and intuitive arguments.

Abstract

We study the Page curve of an evaporating black hole using a toy model given by Jackiw-Teitelboim gravity with Fateev-Zamolodchikov-Zamolodchikov-Teschner (FZZT) antibranes. We treat the anti-FZZT branes as dynamical objects, taking their back-reaction into account. We construct the entanglement entropy from the dual matrix model and study its behavior as a function of the 't Hooft coupling $t$ proportional to the number of branes, which plays the role of time. By numerical computation we observe that the entropy first increases and then decreases as $t$ grows, reproducing the well-known behavior of the Page curve of an evaporating black hole. The system finally exhibits a phase transition, which may be viewed as the end of the evaporation. We study the critical behavior of the entropy near the phase transition. We also make a conjecture about the late-time monotonically decreasing behavior of the entropy. We prove it in a certain limit as well as give an intuitive explanation by means of the dual matrix model.