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arxiv: 1905.08255 · v3 · submitted 2019-05-20 · ✦ hep-th · gr-qc· quant-ph

Entanglement Wedge Reconstruction and the Information Paradox

Geoffrey Penington This is my paper

Pith reviewed 2026-05-18 05:00 UTC · model grok-4.3

classification ✦ hep-th gr-qcquant-ph
keywords black hole evaporationRyu-Takayanagi surfacePage curveentanglement wedgeHawking radiationinformation paradoxAdS/CFTquantum entanglement
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The pith

The quantum Ryu-Takayanagi surface for an evaporating black hole jumps inside the event horizon at the Page time.

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

The paper shows that absorbing boundary conditions for black hole evaporation in AdS/CFT trigger a phase transition in the quantum Ryu-Takayanagi surface exactly at the Page time. After the transition the surface sits slightly inside the horizon at an infalling time set by the scrambling time. This relocation immediately produces the Page curve for black hole entanglement entropy through the Ryu-Takayanagi formula. Entanglement wedge reconstruction then encodes part of the interior in the early radiation, keeping the decreasing entropy consistent with semiclassical late-time Hawking modes and removing the need for a firewall. Reconstructions of interior operators start out state-dependent right after the transition and later apply to wider classes of initial states.

Core claim

When absorbing boundary conditions are used to evaporate a black hole in AdS/CFT, there is a phase transition in the location of the quantum Ryu-Takayanagi surface at precisely the Page time. The new RT surface lies slightly inside the event horizon, at an infalling time approximately the scrambling time β/2π log S_BH into the past. We can immediately derive the Page curve, using the Ryu-Takayanagi formula, and the Hayden-Preskill decoding criterion, using entanglement wedge reconstruction. Because part of the interior is now encoded in the early Hawking radiation, the decreasing entanglement entropy of the black hole is exactly consistent with the semiclassical bulk entanglement of the late

What carries the argument

The phase transition of the quantum Ryu-Takayanagi surface at the Page time, which moves the surface inside the horizon and sets the entanglement wedge for interior reconstruction from radiation.

If this is right

  • The black hole entanglement entropy follows the Page curve after the transition.
  • Interior operators become reconstructible from the Hawking radiation right after the Page time when the initial state is known.
  • Reconstructions later work simultaneously for a large class of initial states as evaporation continues.
  • The radiation volume needed to decode a diary thrown into the black hole depends on both the diary energy and its entropy.
  • Before evaporation starts, a state-independent interior reconstruction exists for any code space whose entropy is strictly less than the Bekenstein-Hawking entropy.

Where Pith is reading between the lines

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

  • The encoding of the interior in early radiation provides a concrete mechanism for information to escape without violating bulk semiclassical physics.
  • The same surface-jump logic may apply to other holographic models that track information flow during evaporation.
  • The tiny non-perturbative errors in reconstruction appear essential for allowing the transition to occur while preserving consistency across states.

Load-bearing premise

The quantum Ryu-Takayanagi formula continues to compute the correct entanglement entropy even after the surface jumps inside the horizon and the bulk is no longer in a simple semiclassical state.

What would settle it

A direct calculation showing that the entanglement entropy stays constant or rises after the Page time, or that the quantum RT surface remains outside the horizon, would falsify the claimed phase transition.

read the original abstract

When absorbing boundary conditions are used to evaporate a black hole in AdS/CFT, we show that there is a phase transition in the location of the quantum Ryu-Takayanagi surface, at precisely the Page time. The new RT surface lies slightly inside the event horizon, at an infalling time approximately the scrambling time $\beta/2\pi \log S_{BH}$ into the past. We can immediately derive the Page curve, using the Ryu-Takayanagi formula, and the Hayden-Preskill decoding criterion, using entanglement wedge reconstruction. Because part of the interior is now encoded in the early Hawking radiation, the decreasing entanglement entropy of the black hole is exactly consistent with the semiclassical bulk entanglement of the late-time Hawking modes, despite the absence of a firewall. By studying the entanglement wedge of highly mixed states, we can understand the state dependence of the interior reconstructions. A crucial role is played by the existence of tiny, non-perturbative errors in entanglement wedge reconstruction. Directly after the Page time, interior operators can only be reconstructed from the Hawking radiation if the initial state of the black hole is known. As the black hole continues to evaporate, reconstructions become possible that simultaneously work for a large class of initial states. Using similar techniques, we generalise Hayden-Preskill to show how the amount of Hawking radiation required to reconstruct a large diary, thrown into the black hole, depends on both the energy and the entropy of the diary. Finally we argue that, before the evaporation begins, a single, state-independent interior reconstruction exists for any code space of microstates with entropy strictly less than the Bekenstein-Hawking entropy, and show that this is sufficient state dependence to avoid the AMPSS typical-state firewall paradox.

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

2 major / 2 minor

Summary. The manuscript claims that in AdS/CFT with absorbing boundary conditions for black hole evaporation, the quantum Ryu-Takayanagi surface undergoes a phase transition precisely at the Page time. The new surface lies slightly inside the event horizon at an infalling time of order the scrambling time β/2π log S_BH. This geometry is used to derive the Page curve for the radiation entanglement entropy via the RT formula, to obtain Hayden-Preskill decoding via entanglement wedge reconstruction, and to analyze state-dependent interior reconstructions that avoid the AMPSS firewall paradox.

Significance. If the central claims hold, the work supplies a geometric mechanism for the Page curve in a controlled evaporating setup and links entanglement wedge reconstruction directly to the information paradox resolution. It also provides concrete statements about the amount of radiation needed for diary reconstruction and the minimal state dependence required to evade typical-state firewalls.

major comments (2)
  1. [§3] §3 (phase transition analysis): the location of the new RT surface is argued from bulk geometry to lie at infalling time ~ β/2π log S_BH inside the horizon, but no explicit bulk calculation is supplied showing that this surface is minimal once the absorbing boundary conditions and ongoing evaporation are included; the transition is asserted to occur exactly at the Page time without a derivation of the jump condition from the generalized entropy functional.
  2. [§4.1] §4.1 (application of quantum RT after transition): the decreasing Page curve is obtained by equating the area of the new interior surface plus bulk entropy term directly to the radiation entropy, yet the manuscript provides no independent check or error estimate that the quantum RT prescription remains valid when the surface is inside the horizon and the bulk is no longer a simple semiclassical geometry.
minor comments (2)
  1. [Introduction] The definition of the scrambling time in the introduction could be cross-referenced to the precise expression used in the bulk geometry calculation.
  2. A brief remark on the regime of validity of the absorbing boundary conditions (e.g., back-reaction size) would help readers assess the semiclassical approximation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for providing constructive comments. We address each of the major comments in turn below. Our responses aim to clarify the reasoning in the paper while acknowledging areas where additional discussion could be beneficial.

read point-by-point responses

  1. Referee: [§3] §3 (phase transition analysis): the location of the new RT surface is argued from bulk geometry to lie at infalling time ~ β/2π log S_BH inside the horizon, but no explicit bulk calculation is supplied showing that this surface is minimal once the absorbing boundary conditions and ongoing evaporation are included; the transition is asserted to occur exactly at the Page time without a derivation of the jump condition from the generalized entropy functional.

    Authors: The location of the quantum RT surface is found by requiring that it extremizes the generalized entropy S_gen = Area/4G + S_bulk. In the geometry of the evaporating black hole with absorbing boundary conditions, the area term grows exponentially with the infalling time due to the blueshift near the horizon, leading to the position at approximately the scrambling time β/2π log S_BH. The transition occurs at the Page time because this is the point where S_gen for the new surface becomes less than that for the original surface, which is how the Page time is defined in this setup. While a full numerical calculation including all backreaction effects from evaporation would be computationally intensive and is not performed, the analytic approximation is justified by the dominance of the near-horizon geometry. We will add a more explicit derivation of the jump condition in the revised manuscript to address this point. revision: partial

  2. Referee: [§4.1] §4.1 (application of quantum RT after transition): the decreasing Page curve is obtained by equating the area of the new interior surface plus bulk entropy term directly to the radiation entropy, yet the manuscript provides no independent check or error estimate that the quantum RT prescription remains valid when the surface is inside the horizon and the bulk is no longer a simple semiclassical geometry.

    Authors: After the phase transition, the quantum RT formula is applied to the new surface, which lies in a region where the curvature is still controlled and the semiclassical approximation for the bulk fields remains valid. The bulk entropy term precisely captures the entanglement entropy of the Hawking radiation modes. The consistency of the resulting Page curve with expectations from quantum information theory provides a check on the validity. However, we agree that an error estimate or discussion of higher-order corrections would be useful. We will include a brief section discussing the regime of validity of the quantum RT prescription in the revised version of the manuscript. revision: partial

Circularity Check

0 steps flagged

No significant circularity; Page curve follows from independent application of quantum RT formula

full rationale

The paper determines the phase transition time by comparing generalized entropies of candidate quantum RT surfaces in the semiclassical bulk geometry under absorbing boundary conditions. The decreasing Page curve is then obtained directly from the area term of the new interior surface via the standard quantum Ryu-Takayanagi prescription taken from prior literature. No equation reduces the output entropy to a fitted parameter, self-referential definition, or load-bearing self-citation within the paper; the identification of the transition with the Page time emerges from the geometry and entropy minimization rather than presupposing the final curve.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the quantum Ryu-Takayanagi formula as an imported domain assumption and on the existence of a phase transition whose location is tied to the scrambling time; no new free parameters or invented entities are introduced beyond the surface itself.

axioms (1)
  • domain assumption The quantum Ryu-Takayanagi formula gives the entanglement entropy of boundary regions via the area of a bulk extremal surface
    Invoked throughout to equate the new surface location with the Page curve entropy after the transition.

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