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.
Highlights
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 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
In this paper we studied the entanglement entropy in the matrix model of JT gravity with anti-FZZT branes, which serves as a toy model of an evaporating black hole
Summary
We will describe our model and explain the general method of computing the entropy of the Hawking radiation. In many parts of our formulation we follow the method of [13] with EOW branes being replaced by anti-FZZT branes. This is along the lines of [25] and an important difference from [13]
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