Universal structure of islands in evaporating black holes

TL;DR

This paper demonstrates that in general black holes, islands relevant to entanglement entropy calculations extend outside the horizon for stationary black holes but are hidden inside for evaporating black holes, revealing a universal structure.

Contribution

It provides a general proof that islands in evaporating black holes are always located inside the horizon, regardless of black hole specifics.

Findings

Islands extend outside the horizon in stationary black holes.

Islands are hidden inside the horizon in evaporating black holes.

The structure of islands is universal across different black hole models.

Abstract

The entanglement entropy of the Hawking radiation contains contributions from a region inside the black hole, which is called islands, implying that the Hawking radiation contains the information of islands. The boundary of the island is given by the quantum extremal surface, whose position is determined so that the entanglement entropy is extremized. In many cases of stationary black holes and a few cases of evaporating black holes, it was already confirmed that the quantum extremal surface is located outside the horizon for stationary black holes and is inside the horizon for evaporating black holes. In this paper, we calculate islands in general black holes and show that the island extends to the outside of the horizon for stationary black holes but is hidden inside the horizon for evaporating black holes independent of details of the black hole.