Page Curve of AdS-Schwarzschild Black Hole by Holographic Boundary Conformal Field Theory

Chia-Jui Chou^1*, Hans Lao¹, Yi Yang¹

¹Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan

* Presenter:Chia-Jui Chou, email:agoodmanjerry@gmail.com

We consider the Hawking evaperation process of a (d+1)-dimensional AdS-Schwarzschild black hole which its states are holographically dual to the states of a d-dimensional Conformal Field Theory (CFT). The states of the black hole is entangled with the states of the Hawking radiation which are represented by the states of a (d+1)-dimensional Boundary Conformal Field Theory (BCFT) which is attached by the d-dimensional CFT dual to the black hole.
By this "Doubly-Holographic" setup, we can calculate the Holographic Entanglement Entropy (HEE) betweent the black hole and the Hawking radiation using Ryu-Takayanagi formula. As more Hawking radiation recieved, the entangling region in the BCFT grows and the HEE goes through a phase trasition to the phase that the entanglement wedge includes part of the (d+1)-dimensional AdS-Schwarzschild spacetime and covers the inside of the horizon. By the entanglement wedge reconstruction, the quantum information inside of the horizon can be extracted and recovered.

Keywords: Hawking Radiation, Information Paradox, Page Curve, Entanglement Entropy, Holography