Universal structure of islands in evaporating black holes

A bstract 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 in the Hartle-Hawking vacuum and a few cases of evaporating black holes in the Unruh vacuum, it was already confirmed that the quantum extremal surface is located outside the horizon for black holes in the Hartle-Hawking vacuum and is inside the horizon for black holes in the Unruh vacuum. In this paper, we calculate islands in general black holes and show that the island extends to the outside of the horizon in the Hartle-Hawking vacuum but is hidden inside the horizon in the Unruh vacuum independent of details of the black hole.