[Paper Review] Islands outside the horizon

Ahmed Almheiri, Raghu Mahajan+1 more|arXiv (Cornell University)|Oct 24, 2019

Black Holes and Theoretical Physics44 references211 citations

TL;DR

The paper analyzes an AdS2 black hole in equilibrium with a bath, showing entanglement wedge islands can lie outside the horizon and are constrained by the quantum focusing conjecture to avoid causality paradoxes, with implications for black hole information in bath-coupled setups.

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.

Motivation & Objective

• Investigate how entanglement wedge islands can extend outside black hole horizons when an AdS2 black hole is in equilibrium with a bath.
• Compute von Neumann entropies for both the black hole degrees of freedom and the bath, including island contributions.
• Examine potential causality issues and show how the quantum focusing conjecture (QFC) resolves them.
• Formulate and analyze an information paradox variant for a black hole in a bath in the Hartle-Hawking state, highlighting the island's role in resolution.

Proposed method

• Use Jackiw-Teitelboim gravity coupled to a conformal matter CFT to model nearly-AdS2 black holes in contact with a bath.
• Compute generalized entropy S_gen = S_bulk + (Area/4G_N) for candidate islands and extremize to locate quantum extremal surfaces.
• Demonstrate, via explicit extremization, that the quantum extremal surfaces can lie outside the horizon and interpret in terms of entanglement wedges.
• Invoke the quantum focusing conjecture (QFC) to argue causality is preserved despite island outside-horizon location.
• Extend to finite temperature cases and analyze how the thermofield double/Hartle-Hawking state shapes island behavior and information flow.

Experimental results

Research questions

• RQ1 Do islands extend outside the black hole horizon in AdS2 setups coupled to a bath, and under what conditions?
• RQ2 How does the generalized entropy incorporating islands behave in extremal and nonzero temperature cases?
• RQ3 Can the quantum focusing conjecture (QFC) prevent causality paradoxes when islands lie outside horizons?
• RQ4 How do islands affect information flow and resolve information paradoxes in a black hole coupled to a bath in the Hartle-Hawking state?

Key findings

• Islands can extend outside the black hole horizon in both extremal and nonzero temperature AdS2 setups coupled to a bath.
• The generalized entropy S_gen, including island contributions, is extremized to determine the entanglement wedge, with the island often located outside the horizon.
• The QFC ensures causality is preserved, preventing signals from islands from contradicting boundary causality after decoupling procedures.
• In the Hartle-Hawking state, islands help resolve a version of the information paradox by balancing entanglement growth with island contributions.
• The analysis connects near-horizon physics to long-distance bath correlations, indicating the island degrees of freedom can be encoded in exterior regions.