SciPost Submission Page

Entanglement islands in higher dimensions

by Ahmed Almheiri, Raghu Mahajan, Jorge E. Santos

Submission summary

As Contributors: Raghu Mahajan
Arxiv Link:
Date submitted: 2020-01-14
Submitted by: Mahajan, Raghu
Submitted to: SciPost Physics
Discipline: Physics
Subject area: High-Energy Physics - Theory
Approaches: Theoretical, Computational


It has been suggested in recent work that the Page curve of Hawking radiation can be recovered using computations in semi-classical gravity provided one allows for "islands" in the gravity region of quantum systems coupled to gravity. The explicit computations so far have been restricted to black holes in two-dimensional Jackiw-Teitelboim gravity. In this note, we numerically construct a five-dimensional asymptotically AdS geometry whose boundary realizes a four-dimensional Hartle-Hawking state on an eternal AdS black hole in equilibrium with a bath. We also numerically find two types of extremal surfaces: ones that correspond to having or not having an island. The version of the information paradox involving the eternal black hole exists in this setup, and it is avoided by the presence of islands. Thus, recent computations exhibiting islands in two-dimensional gravity generalize to higher dimensions as well.

Current status:
Editor-in-charge assigned

Submission & Refereeing History

Submission 1911.09666v2 on 14 January 2020

Reports on this Submission

Anonymous Report 1 on 2020-2-12 Invited Report


1- Clear, well-motivated, and interesting goal (find island in higher dimensional BH setup).
2- Good, logical explanation of method and results.


1- Does not discuss the existing higher dimensional analysis in their reference 12, by Penington.
2- Unclear why the RS brane is allowed to have RT surface dynamically end on it and yet be considered part of the `boundary.’


This is a thorough, clear analysis that answers an interesting question. The authors have done a service for the field by writing this up.

Two comments:
There could be some improvement in how these results are related to prior work. In particular, in reference [12], Penington argues for the existence of these islands in general dimensions. While he does make simplifying assumptions (spherical symmetry), his arguments are relevant to the goal of this paper and should be acknowledged.

How are we supposed to understand the seemingly-inconsistent treatment of the RS brane? Sometimes it acts like part of the "bulk’’ (because the RT surface is allowed to end on it at a dynamical location), and other times it acts like part of the "boundary’’ (because its degrees of freedom are understood to be entangled with the "true boundary’’ degrees of freedom). Is one of these interpretations more correct, e.g. that it should only be understood as part of the bulk (in which case how do we understand its entanglement with the "true boundary’’)? Or perhaps is the answer unknown, and you are simply demonstrating that treating the RS brane this way gives an interesting answer?

Requested changes

1- Add a sentence or two about Penington’s higher-dimensional island arguments. If what you are doing is more impressive for certain reasons, mention!
2- Add a couple sentences or a footnote about how we should think of the RS brane. As part of the bulk, part of the boundary, or somehow both?

  • validity: high
  • significance: high
  • originality: high
  • clarity: top
  • formatting: perfect
  • grammar: perfect

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