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Islands and stretched horizon
Yoshinori Matsuo
Résumé : Recently it was proposed that the entanglement entropy of the Hawking radiation reflects the information of a region including the interior of the event horizon, so-called island. This also implies that the information of the complement of the Hawking radiation, which is nothing but the black hole, is not placed inside the event horizon, at least after the Page time. We study the entanglement entropy of the black hole as the complement of the Hawking radiation, in the eternal Schwarzschild black hole in four-dimensional asymptotically flat spacetime. Although the entanglement entropy of the black hole before the Page time is given by that of a region including the interior of the event horizon, it can be interpreted as a consequence of the replica trick in gravitational theories, in a similar fashion to the island for the Hawking radiation. By comparing it with the maximally extended island, the information of the black hole is considered to be localized on a surface near the event horizon, which can be understood as the stretched horizon. This structure also resembles the case of black holes in the AdS spacetime with auxiliary flat spacetime, where the information of the black hole is localized at the interface between the AdS spacetime and the flat spacetime.