Unitarity from a smooth horizon?
Raphael Bousso, Marija Tomašević
Abstract
Under semiclassical evolution, black holes retain a smooth horizon but fail to return information. Yet, the Ryu-Takayanagi (RT) prescription computes the boundary entropy expected from unitary conformal field theory (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 $\mathrm{AdS}/\mathrm{CFT}$ dictionary. (ii) No unique quantum field theory 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 find: the ensemble average of out states would be mixed, but the ensemble average of final entropies would vanish.