Page curve from dynamical branes in JT gravity

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.

Page curve of AdS-Vaidya model for evaporating black holes

“…There were many proposals to try and alleviate the issues posed by the information paradox [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Among the proposals, one route that has taken much attention is through the Ryu and Takayanagi (RT) prescription which studies the fine-grained entropy in a geometrical context through the AdS/CFT correspondence, albeit only for time-independent cases [23,24].…”