Unitarity From a Smooth Horizon?

TL;DR

The paper investigates how the Ryu-Takayanagi prescription can yield boundary entropies consistent with unitary evolution in a semiclassical bulk where information appears to be lost. By introducing a large Dyson-sphere detector that absorbs Hawking radiation without auxiliary systems, it shows RT reproduces a Page-curve-like boundary behavior without assuming entanglement-wedge complementarity, while also highlighting tensions with the extrapolate dictionary. It then analyzes multiple interpretations, including bulk information loss vs. boundary unitarity, potential ambiguities in asymptotic bulk states, and nonlocal detector effects, arguing that full consistency may require firewall-like bulk breakdowns or an ensemble of dual theories. The discussion suggests that RT results constrain where semiclassical gravity can remain valid and points toward possible resolutions involving nonlocality, ensemble duals, or horizon-level new physics.

Abstract

Under semiclassical evolution, black holes retain a smooth horizon but fail to return information. Yet, the Ryu-Takayanagi prescription computes the boundary entropy expected from unitary CFT evolution. We demonstrate this in a novel setting with an asymptotic bulk detector, eliminating an assumption about the entanglement wedge of auxiliary systems. We consider three interpretations of this result. (i) At face value, information is lost in the bulk but not in the CFT. This conflicts with the AdS/CFT dictionary. (ii) No unique QFT state (pure or mixed) governs all detector responses to the bulk Hawking radiation. This conflicts with the existence of an S-matrix. (iii) Nonlocal couplings to the black hole interior cause asymptotic detectors to respond as though the radiation was pure, even though it is naively thermal. This invalidates the standard interpretation of the semiclassical state, including its smoothness at the horizon. We conclude that unitary boundary evolution requires asymptotic bulk detectors to become unambiguously pure at late times. We ask whether the RT prescription can still reproduce the boundary entropy in this bulk scenario. We find that this requires a substantial failure of semiclassical gravity in a low-curvature region, such as a firewall that purifies the Hawking radiation. Finally, we allow that the dual to semiclassical gravity may be an ensemble of unitary theories. This appears to relax the tensions we found: the ensemble average of out-states would be mixed, but the ensemble average of final entropies would vanish.

Figures (5)

• Figure 1: Semiclassical bulk evolution of a black hole in AdS with global boundary $R$. The Hawking radiation is absorbed into an auxiliary system Pen19AEMM. The entanglement wedges $EW(R)$ and $EW({\rm aux})$ are shown (a) before and (b) after the Page time. Entanglement wedge complementarity is assumed here but will not be needed in the setting we describe in Sec. \ref{['sec-dyson']}.
• Figure 2: Formation and evaporation of a black hole in AdS. The Hawking radiation is absorbed into a Dyson sphere near the boundary. The bulk evolution is computed semiclassically. Nevertheless, the Ryu-Takayanagi prescription yields a boundary entropy consistent with unitary boundary evolution. However, energetic arguments and the extrapolate dictionary imply that the semiclassical bulk state at late times cannot have a pure-state boundary dual (see Sec. \ref{['sec-interpretations']}). This conclusion depends only on the largeness of the entropy of the Hawking radiation in the bulk. Because the Dyson sphere can be probed with arbitrarily dilute local operators, even complicated bulk probes of the Dyson sphere do not engender large gravitational backreaction, and standard QFT rules should apply.
• Figure 3: In a semiclassically evolved bulk state, the Hawking radiation is absorbed and transferred to a near-boundary reservoir, localized to a small angle. $R$ is a boundary region near the reservoir. (a) At $t_1<t_{\rm Page}$, the entanglement wedge $EW(R)$ includes only the reservoir. (b) At $t_2>t_{\rm Page}$, the minimal quantum extremal surface $\gamma$ has a second component near the black hole horizon. $EW(R)$ now contains the black hole interior.
• Figure 4: Up to a constant contribution from vacuum entanglement between $R$ and $\bar{R}$, the entropy of the two complementary boundary regions follows a Page curve. From the boundary point of view, this is because a system is slowly transferred from $\bar{R}$ to $R$. The RT prescription reproduces this curve from a bulk geometry obtained by semiclassical bulk evolution. However, this bulk dual is again inconsistent with the extrapolate dictionary (see Sec. \ref{['sec-interpretations']}).
• Figure 5: The entanglement wedge of a boundary region $R$ consisting of two components. Near-boundary particles are purified by particles deep in the bulk. This is consistent with a low-entropy state of $R$, since the deep particles have an energetic imprint on the boundary. Hence dilute CFT degrees of freedom are available to purify the more localized excitations. By contrast, bulk excitations behind a black hole horizon leave no energetic imprint near infinity, so there need not be enough states available in the CFT to represent them.