Mutual information, islands in black holes and the Page curve

Abstract

The role played by the mutual information of subsystems on the Page curve is explored in this paper. With the total system consisting of the black hole and radiation, together with the inclusion of island, we observe that the vanishing of mutual information between $B_{+}$ and $B_{-}$ which in turn means the disconnected phase of the entanglement wedge corresponding to $B_{+}\cup B_{-}$, yields a time scale of the order of scrambling time. This results in a time independent expression for the fine grained entropy of Hawking radiation consistent with the correct Page curve. We also find corrections to this entropy and Page time which are logarithmic and inverse power law in form.

arXiv commentv1: 5 pages LaTex and 1 figure, v2: 9 pages Latex and 1 figure, v3: Additional comments have been added, to appear in EPJC

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• Small Schwarzschild de Sitter black holes, quantum extremal surfaces and islands
• Entanglement Islands in Generalized Two-dimensional Dilaton Black Holes
• Massless Entanglement Islands in Cone Holography
• The role of mutual information in the Page curve
• Cosmological and black hole islands in multi-event horizon spacetimes
• Planar Black Holes in Holographic Axion Gravity: Islands, Page Times, and Scrambling Times
• Island on codimension-two branes in AdS/dCFT
• Unitary Constraints on Semiclassical Schwarzschild Black Holes in the Presence of Island
• Page Curves of Reissner-Nordström Black Hole in HD Gravity
• Island formula in Planck brane
• Defect extremal surfaces for entanglement negativity
• Mutual information of subsystems and the Page curve for Schwarzschild de-Sitter black hole
• Page curves and Entanglement Islands for the Step-Function Vaidya Model of Evaporating Black Holes
• Islands in Kerr-de Sitter spacetime and their flat limit
• Page Curve for Eternal Schwarzschild Black Hole in Dimensionally-Reduced Model of Dilaton Gravity
• Reflected Entropy and Entanglement Negativity for Holographic Moving Mirrors
• Page Curve of AdS-Vaidya Model for Evaporating Black Holes
• Effect of backreaction on Island, Page curve and Mutual Information
• Investigating the role of mutual information in the Page curve for a functional renormalization group improved Schwarzschild black hole
• New insights on mutual information in the island approach to the Page curve