Page curve from dynamical branes in JT gravity

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.

Automated summary

In this study, a toy model is used to investigate the Page curve of an evaporating black hole. It is observed that the entropy first increases and then decreases over time, reproducing the well-known behavior of the Page curve. The system undergoes a phase transition, marking the end of the evaporation. A conjecture about the late-time monotonically decreasing behavior of the entropy is proposed and supported by evidence from a certain limit and the dual matrix model.