Page Curve of Effective Hawking Radiation

Abstract

We study the generalized entanglement entropy in the higher dimensional two-sided eternal black hole by double holography. By introducing an end-of-the-world ETW brane, which defines the time-dependent effective Hawking radiation region, we find a new type of Ryu-Takayanagi surface besides the Hartman-Maldacena surface and the island Ryu-Takayanagi surface known previously. We study the phase transition among the three Ryu-Takayanagi surfaces at different temperatures and obtain the phase diagram as well as the Page curve.

Definitions and descriptions were clarified in sections 2.4 and 3.2, modified some diagrams and added more for clarification, added more detailed calculations in section 3.2, corrected some minor typos

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• Defect extremal surfaces for entanglement negativity
• Island formula in Planck brane
• Ghost Problem, Spectrum Identities and Various Constraints on Brane-localized Gravity
• Black holes Entangled by Radiation
• Page Curve of AdS-Vaidya Model for Evaporating Black Holes
• Cone Holography with Neumann Boundary Conditions and Brane-localized Gauge Fields
• Entanglement inside a black hole before the Page time
• Effect of backreaction on Island, Page curve and Mutual Information