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.
Highlights
We find that the bulk analysis reproduces this, for the simple reason that there is no nontrivial quantum extremal surface (QES) at any time, and that the global bulk state ρHawking is pure
II we reproduced the results of Refs. [17,18] in a setting that eliminates a key assumption about entanglement wedge complementarity
By applying the quantumcorrected RT prescription to a bulk state obtained from semiclassical evolution, we found that appropriate boundary regions obey the Page curve, consistent with unitary boundary evolution
Summary
The information paradox was first formulated for black holes in asymptotically flat spacetime. HTμνi 1⁄4 TrðρTμνÞ, where ρ 1⁄4 ρHawking is the global state of the quantum fields If effective field theory is valid outside the horizon, a pure out-state implies that a freely falling observer encounters large excitations (a “firewall”) at the horizon of an arbitrarily large black hole, at least after the Page time [3,4]. An interesting class of approaches [5,6,7] constructs effective interior operators consistent with a smooth horizon This works only for certain classes of states, and only at the cost of introducing significant nonlinearity in the form of state dependence [8,9,10,11]. Whether these ideas can be developed into a consistent framework that preserves both unitarity and the equivalence principle. (See Refs. [12,13,14] for some challenges; see Ref. [15] for a review and further references.)
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