Islands outside the horizon

TL;DR

This paper investigates entanglement islands outside black hole horizons in an AdS$_2$ setup, revealing implications for causality and the black hole information paradox, and demonstrating how islands help resolve paradoxes in black hole physics.

Contribution

It introduces the concept of islands extending outside the horizon and explores their role in causality and information paradox resolution.

Findings

Islands can extend outside the black hole horizon.

Quantum focusing conjecture prevents causality paradoxes.

Islands are crucial in resolving the black hole information paradox.

Abstract

We consider an AdS$_2$ black hole in equilibrium with a bath, which we take to have a dual description as (0+1)-dimensional quantum mechanical system coupled to a (1+1)-dimensional field theory serving as the bath. We compute the entropies of both the quantum mechanical degrees of freedom and of the bath separately, while allowing contributions from entanglement wedge "islands". We find situations where the island extends {\it outside} the black hole horizon. This suggests possible causality paradoxes which we show are avoided because of the quantum focusing conjecture. Finally, we formulate a version of the information paradox for a black hole in contact with a bath in the Hartle-Hawking state, and demonstrate the role of islands in resolving this paradox.