The role of mutual information in the Page curve

Abstract

In this letter, we give two proposals regarding the status of connectivity of entanglement wedges and the associated saturation of mutual information. The first proposal has been given for the scenario before the Page time depicting the fact that the early to late time transition can be obtained from the status of the radiation entanglement wedge. In particular, we compute the time where the mutual information between the regions where the Hawking radiation gets collected vanishes before the formation of the island. We argue that this time is the Hartman-Maldacena time at which the fine-grained entropy of radiation goes as ∼ log(β) where β is the inverse of Hawking temperature of the black hole. On the other hand, the second proposal probes the crucial role played by the mutual information of black hole subsystems in obtaining the correct Page curve of radiation.

Small Schwarzschild de Sitter black holes, quantum extremal surfaces and islands

“…The timelike separation implies that the generalized entropy becomes complex-valued, with log(−|∆ 2 |) giving rise to log(−1) = iπ, as in pure de Sitter. Now, by putting ω = ω 0 in (E 90). givesThe future boundary observer has r = ∞ and τ 0 = 0 so y 0 = 0.…”

Massless Entanglement Islands in Cone Holography

“…Remarkably, [29] finds that the massless island puzzle can be resolved, provided that the bulk state breaks all asymptotic symmetries. See also [30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63] for some recent works on entanglement islands, Page curve and AdS/BCFT.…”