  Recently it was proposed that the entanglement entropy of the Hawking
radiation contains the information of a region including the interior of the
event horizon, which is called "island." In studies of the entanglement entropy
of the Hawking radiation, the total system in the black hole geometry is
separated into the Hawking radiation and black hole. In this paper, we study
the entanglement entropy of the black hole in the asymptotically flat
Schwarzschild spacetime. Consistency with the island rule for the Hawking
radiation implies that the information of the black hole is located in a
different region than the island. We found an instability of the island in the
calculation of the entanglement entropy of the region outside a surface near
the horizon. This implies that the region contains all information of the total
system and the information of the black hole is localized on the surface. Thus
the surface would be interpreted as the stretched horizon. This structure also
resembles black holes in the AdS spacetime with an auxiliary flat spacetime,
where the information of the black hole is localized at the interface between
the AdS spacetime and the flat spacetime.
