Mutual information of subsystems and the Page curve for Schwarzschild de-Sitter black hole

Abstract

In this work, we show that the two proposals associated to the mutual information of matter fields can be given for an eternal Schwarzschild black hole in de-Sitter spacetime. These proposals also depicts the status of associated entanglement wedges and their roleplay in obtaining the correct Page curve of radiation. The first proposal has been give for the before Page time scenario, which shows that the mutual information $I(R_H^{+}:R_H^{-})$ vanishes at a certain value of the observer's time $t_{b_H}=t_H$ (where $t_H\ll {\beta }_H$). We claim that this is the Hartman-Maldacena time at which the entanglement wedge associated to $R_H^{+}\cup R_H^{-}$ gets disconnected and the fine-grained radiation entropy has the form $S(R_H)\sim \log ({\beta }_H)$. The second proposal depicts the fact that just after the Page time, when the replica wormholes are the dominating saddle-points, the mutual information $I(B_H^{+}:B_H^{-})$ vanishes as soon as the time difference $t_{a_H}-t_{b_H}$ equals the scrambling time. Holographically, this reflects that the entanglement wedge associated to $B_H^{+}\cup B_H^{-}$ jumps to the disconnected phase at this particular time-scale. Furthermore, these two proposals lead us to the correct time-evolution of the fine-grained entropy of radiation as portrayed by the Page curve. We have also shown that similar observations can be obtained for the radiation associated to the cosmological horizon.

v1:18 pages LaTex with multiple figures, v2: matches with the accepted version; To appear in Physical Review D

References in corpus (28)

• Black holes as mirrors: quantum information in random subsystems
• Thermodynamics of de Sitter Black Holes: Thermal Cosmological Constant
• Inconsistency of Islands in Theories with Long-Range Gravity
• An Information Paradox and Its Resolution in de Sitter Holography
• Islands in Asymptotically Flat 2D Gravity
• Gravity/Ensemble Duality
• Holographic BCFTs and Communicating Black Holes
• Notes on islands in asymptotically flat 2d dilaton black holes
• Entanglement Phase Structure of a Holographic BCFT in a Black Hole Background
• Failure of the split property in gravity and the information paradox
• The universality of islands outside the horizon
• Quantum Extremal Islands Made Easy, Part IV: Massive Black Holes on the Brane
• Island, Page Curve and Superradiance of Rotating BTZ Black Holes
• Entanglement Island and Page Curve in Wedge Holography
• Mutual information, islands in black holes and the Page curve
• AdS/BCFT and Island for curvature-squared gravity
• Small Schwarzschild de Sitter black holes, quantum extremal surfaces and islands
• Entanglement Islands in Generalized Two-dimensional Dilaton Black Holes
• 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
• Entanglement degradation in multi-event horizon spacetimes
• 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
• Page curves and Entanglement Islands for the Step-Function Vaidya Model of Evaporating Black Holes
• Holographic study of entanglement and complexity for mixed states
• Entanglement wedge cross section for noncommutative Yang-Mills theory

Cited by in corpus (6)

• Entanglement entropy analysis of dyonic black holes using doubly holographic theory
• Island formula in Planck brane
• Genuine four-partite Bell nonlocality in the curved spacetime
• 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