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arxiv: 1905.08762 · v3 · submitted 2019-05-21 · ✦ hep-th · gr-qc

The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole

Ahmed Almheiri , Netta Engelhardt , Donald Marolf , Henry Maxfield This is my paper

Pith reviewed 2026-05-18 04:44 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords black hole evaporationquantum extremal surfacesgeneralized entropyentanglement wedgeJackiw-Teitelboim gravityPage timeHayden-Preskill protocol
0
0 comments X

The pith

Bulk quantum entropy gradients shift the quantum extremal surface so that an evaporating black hole's entanglement wedge loses ingoing information after a scrambling time.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper models one-sided evaporation of a two-sided black hole in Jackiw-Teitelboim gravity coupled to a 1+1 conformal field theory by attaching an auxiliary heat sink to one boundary. Large boosts in the geometry produce order-1/G_N gradients in the bulk von Neumann entropy of quantum fields. These gradients move the quantum extremal surface far from any classical extremal surface and determine the generalized entropy. The resulting entanglement wedge loses access to information sent into the black hole after a time of order the scrambling time, matching expectations from unitarity and the Hayden-Preskill protocol. A phase transition in the location of the quantum extremal surface also appears near the Page time of the evaporation process.

Core claim

In this two-boundary 2d bulk system, the generalized entropy evaluated at the quantum extremal surface behaves as required by unitarity. Ingoing information disappears from the entanglement wedge after a scrambling time β/2π ln ΔS + O(1), in accord with holographic implementations of the Hayden-Preskill protocol. An interesting phase transition in the quantum extremal surface occurs at what one might call the Page time for the process.

What carries the argument

The quantum extremal surface that extremizes the generalized entropy A/4G_N + S_bulk, whose location is controlled by O(1/G_N) gradients in S_bulk generated by large boosts in the evaporating geometry.

If this is right

  • The generalized entropy at the quantum extremal surface follows the time dependence required by unitarity during evaporation.
  • Ingoing information is excluded from the entanglement wedge after a scrambling time β/2π ln ΔS + O(1).
  • A phase transition occurs in the quantum extremal surface at the Page time of the evaporation.
  • The bulk entropy contribution can dominate the location of the surface despite being formally subleading in 1/G_N.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar entropy-gradient effects could appear in higher-dimensional models of evaporating black holes once large boosts are included.
  • The phase transition at the Page time may mark the moment when the radiation begins to encode the interior in a unitary way.
  • The construction supplies a concrete setting in which to test whether other information-recovery protocols produce the same scrambling-time delay.

Load-bearing premise

The two-boundary 2d bulk system of Jackiw-Teitelboim gravity coupled to a 1+1 CFT remains a valid holographic description when coupled to an external auxiliary heat sink that induces one-sided evaporation.

What would settle it

An explicit calculation in the same model showing that information remains accessible in the entanglement wedge past the predicted scrambling time β/2π ln ΔS + O(1) would falsify the central claim.

read the original abstract

Bulk quantum fields are often said to contribute to the generalized entropy $\frac{A}{4G_N} +S_{\mathrm{bulk}}$ only at $O(1)$. Nonetheless, in the context of evaporating black holes, $O(1/G_N)$ gradients in $S_{\mathrm{bulk}}$ can arise due to large boosts, introducing a quantum extremal surface far from any classical extremal surface. We examine the effect of such bulk quantum effects on quantum extremal surfaces (QESs) and the resulting entanglement wedge in a simple two-boundary $2d$ bulk system defined by Jackiw-Teitelboim gravity coupled to a 1+1 CFT. Turning on a coupling between one boundary and a further external auxiliary system which functions as a heat sink allows a two-sided otherwise-eternal black hole to evaporate on one side. We find the generalized entropy of the QES to behave as expected from general considerations of unitarity, and in particular that ingoing information disappears from the entanglement wedge after a scambling time $\frac{\beta}{2\pi} \ln \Delta S + O(1)$ in accord with expectations for holographic implementations of the Hayden-Preskill protocol. We also find an interesting QES phase transition at what one might call the Page time for our process.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper studies bulk quantum field contributions to generalized entropy in an evaporating black hole within a two-boundary 2d holographic model of Jackiw-Teitelboim gravity coupled to a 1+1 CFT. One boundary is coupled to an external auxiliary heat sink to induce one-sided evaporation of an otherwise eternal black hole. The authors compute the quantum extremal surface (QES) and report that its generalized entropy follows unitary expectations: ingoing information disappears from the entanglement wedge after a scrambling time β/2π ln ΔS + O(1), consistent with holographic Hayden-Preskill, and a QES phase transition occurs at the Page time for the process.

Significance. If the central results hold, the work supplies a controlled holographic example in which O(1/G_N) gradients in S_bulk arise from large boosts and shift the QES away from classical extremal surfaces, yielding explicit agreement with unitary Page-curve expectations. This strengthens the quantum extremal surface prescription for evaporating black holes and provides a concrete realization of information recovery in a simple 2d model.

major comments (1)
  1. [Model setup] Model setup (abstract and opening sections): The central claim that O(1/G_N) gradients in S_bulk control the QES location and produce the reported scrambling time and Page-time transition rests on the assumption that coupling one boundary to the auxiliary heat sink leaves the JT+CFT holographic dictionary intact. The manuscript must demonstrate explicitly that this coupling does not induce uncontrolled backreaction on the dilaton or metric, nor alter the bulk field content in the boosted regions, since any such modification would shift the QES and invalidate the unitary-behavior match.
minor comments (1)
  1. [Abstract] Abstract: 'scambling time' is a typographical error and should read 'scrambling time'.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address the major comment below, providing a point-by-point response and indicating where revisions will be made to strengthen the presentation.

read point-by-point responses

  1. Referee: Model setup (abstract and opening sections): The central claim that O(1/G_N) gradients in S_bulk control the QES location and produce the reported scrambling time and Page-time transition rests on the assumption that coupling one boundary to the auxiliary heat sink leaves the JT+CFT holographic dictionary intact. The manuscript must demonstrate explicitly that this coupling does not induce uncontrolled backreaction on the dilaton or metric, nor alter the bulk field content in the boosted regions, since any such modification would shift the QES and invalidate the unitary-behavior match.

    Authors: We agree that an explicit demonstration of controlled backreaction is necessary to support the central claims. In our model the auxiliary heat sink is introduced by modifying the boundary conditions on one asymptotic boundary of the JT geometry while leaving the bulk equations of motion and the 1+1 CFT field content unchanged in the interior. The resulting energy flux is accounted for entirely through the boundary dynamics of the dilaton, which remains consistent with the standard JT holographic dictionary. Large boosts that generate the O(1/G_N) gradients in S_bulk are produced by the evaporating geometry itself and are not sourced by the boundary coupling. Nevertheless, to address the referee's request for greater explicitness, we will add a short subsection in the model-setup section that (i) states the precise boundary conditions used for the heat-sink coupling, (ii) shows that any induced metric or dilaton perturbations remain O(1) and do not propagate into the boosted regions at leading order in 1/G_N, and (iii) confirms that the bulk CFT spectrum is unaltered. These additions will be included in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No circularity: QES location and entropy behavior derived from explicit JT+CFT calculation

full rationale

The paper defines a concrete two-boundary JT gravity plus 1+1 CFT model, introduces an auxiliary heat sink coupling on one boundary to induce evaporation, and computes the quantum extremal surface by minimizing the generalized entropy functional that includes the bulk entropy contribution with large-boost gradients. The reported scrambling time β/2π ln ΔS + O(1) and the Page-time phase transition are outputs of this minimization rather than inputs or self-referential definitions. No load-bearing step reduces to a fitted parameter renamed as prediction, a self-citation chain, or an ansatz smuggled from prior work by the same authors. The derivation remains self-contained against the model's own equations and standard holographic entropy prescriptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard holographic duality and the validity of the JT gravity plus CFT model under evaporation; no new free parameters or invented entities are introduced in the abstract description.

axioms (1)
  • domain assumption Holographic correspondence equates boundary entanglement entropy with bulk generalized entropy including quantum field contributions.
    Invoked to interpret the generalized entropy of the quantum extremal surface as controlling the entanglement wedge.

pith-pipeline@v0.9.0 · 5775 in / 1511 out tokens · 46896 ms · 2026-05-18T04:44:44.349366+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • Foundation.DimensionForcing alexander_duality_circle_linking unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    We find the generalized entropy of the QES to behave as expected from general considerations of unitarity, and in particular that ingoing information disappears from the entanglement wedge after a scrambling time β/2π ln ΔS + O(1) in accord with expectations for holographic implementations of the Hayden-Preskill protocol. We also find an interesting QES phase transition at what one might call the Page time for our process.

  • Foundation.LedgerForcing conservation_from_balance unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    Turning on a coupling between one boundary and a further external auxiliary system which functions as a heat sink allows a two-sided otherwise-eternal black hole to evaporate on one side.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
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The paper appears to rely on the theorem as machinery.
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Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

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