Islands and stretched horizon

TL;DR

This paper investigates the entanglement entropy of black holes in flat spacetime, revealing that the black hole's information is localized on a stretched horizon rather than an island, contrasting with previous AdS-based models.

Contribution

It demonstrates that in asymptotically flat Schwarzschild spacetime, the black hole's information resides on a surface near the horizon, challenging the island paradigm and proposing a stretched horizon interpretation.

Findings

Instability of the island near the horizon surface.

Black hole information is localized on a surface, interpreted as the stretched horizon.

Resembles black hole models in AdS with an interface between spacetimes.

Abstract

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.