The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole (1905.08762v3)

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.

• The paper introduces a two-dimensional JT gravity model coupled with a 1+1 CFT to simulate evaporating black holes and analyze quantum extremal surfaces.
• The paper demonstrates that a novel quantum extremal surface captures the transition from entropy growth to decline, aligning with Hayden-Preskill and Page curve predictions.
• The paper challenges semi-classical models by revealing quantum corrections that enforce unitarity and offer new insights into holographic information recovery.

An Expert Overview of "The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole"

The paper by Almheiri, Engelhardt, Marolf, and Maxfield explores the intricate dynamics of quantum extremal surfaces (QESs) in the context of evaporating black holes using a two-dimensional Jackiw-Teitelboim gravity model coupled to a 1+1 conformal field theory (CFT). The central theme of this paper is to investigate how bulk quantum fields affect QESs and the entanglement wedge of an evaporating black hole, and to verify if these features align with unitary quantum mechanical expectations, particularly in the context of the famous information paradox.

Summary of Key Findings

1. Evaporating Black Hole Model: The researchers focus on a two-sided AdS$_2$ black hole that interacts with an auxiliary system acting as a bath. By coupling one side of the black hole to this bath, they effectively paper the evaporation of a black hole that emits radiation, thus allowing the paper of Hawking radiation in a lower-dimensional setting.
2. Quantum Extremal Surfaces and Generalized Entropy: The paper demonstrates how a new, significant role is played by quantum extremal surfaces in tracking the generalized entropy during black hole evaporation. It highlights that, despite being perturbative in nature, the methods capture non-trivial quantum effects on the entropic budget of the black hole.
3. Hayden-Preskill Protocol and Page Curve: The paper finds that the behavior of the QESs closely aligns with the predictions of the Hayden-Preskill protocol. Initially, the entropy associated with the QESs rises due to information being encoded in outgoing Hawking radiation. After the Page time, a new QES displaces the original one, indicating a decrease in entropy consistent with the expected Page curve. This delineates the temporary information retention before eventual retrieval, rendering insights into the holographic nature of black hole information recovery processes.
4. Novel QES and Information Dynamics: The discovery of a novel type of QES, shaped by $O(1/G_N)$ gradients in the entropy of bulk quantum fields, exemplifies how information dynamics in black holes are dictated by quantum effects beyond classical extremal surfaces. This new QES, moving in a spacelike but nearly-null trajectory, aids in recovering the Page curve, effectively demonstrating blackhole information preservation and retrieval in holographically dual settings.
5. Implications on Complementarity and Bulk Reconstruction: By addressing quantum corrections and entropy exchanges, this research challenges and informs the discourse on black hole complementarity and the incompleteness of semi-classical descriptions, especially beyond Page time. It raises relevant questions about how additional structure beyond semi-classical perturbations needs to be integrated for reconciling entropy predictions with unitary evolution.

Theoretical and Practical Implications

The paper has significant implications both theoretically and practically. Theoretically, it strengthens the hypothesis that quantum information in black holes, when viewed through holography, aligns intricately with foundational principles of quantum mechanics, including unitarity. Practically, this work sets a precedent for exploring black hole microstates and entropy dynamics using simpler, more tractable two-dimensional models, which could offer new insights into higher-dimensional settings or experimental realizations in quantum simulations.

Future Directions

Building on these results, future research could extend the investigation into higher-dimensional frameworks or employ numerical simulations to probe deep into the non-perturbative regimes. Additionally, extending the analysis to more complex configurations, such as rotating or charged black holes, could further illuminate the nuanced interplay of gravitational dynamics and quantum information theory. There is also a potential avenue for exploring the nuances of entropy dynamics concerning thermodynamic properties of longer-lived black holes under varied environmental interactions.

In conclusion, the paper by Almheiri et al. represents a substantial advancement in understanding black hole quantum extremal surfaces and their role in resolving the black hole information paradox through holographic principles. The implications of this research resonate deeply within the fields of quantum gravity and holography, prompting a reevaluation of longstanding assumptions about the quantum mechanics of black holes.