Abstract
We investigate the possibility that the geometry dual to a typical AdS black hole microstate corresponds to the extended AdS-Schwarzschild geometry, including a region spacelike to the exterior. We argue that this region can be described by the mirror operators, a set of state-dependent operators in the dual CFT. We probe the geometry of a typical state by considering state-dependent deformations of the CFT Hamiltonian, which have an interpretation as a one-sided analogue of the Gao-Jafferis-Wall traversable wormhole protocol for typical states. We argue that the validity of the conjectured bulk geometry requires that out-of-time-order correlators of simple CFT operators on typical pure states must exhibit the same chaotic effects as thermal correlators at scrambling time. This condition is related to the question of whether the product of operators separated by scrambling time obey the Eigenstate Thermalization Hypothesis. We investigate some of these statements in the SYK model and discuss similarities with state-dependent perturba- tions of pure states in the SYK model previously considered by Kourkoulou and Maldacena. Finally, we discuss how the mirror operators can be used to implement an analogue of the Hayden-Preskill protocol.
Highlights
The black hole information paradox is a long-standing open problem, which is related to the smoothness of the black hole horizon [1, 2]
This condition is related to the question of whether the product of operators separated by scrambling time obey the Eigenstate Thermalization Hypothesis
The observer can prepare an experimental device that acts with the operators O relevant for that microstate and apply them to one of the identically prepared copies which has not been previously measured. Using these state-dependent perturbations by mirror operators, we argue that the consistency of the space-time geometry proposed in this paper, and shown in figure 1, requires as a necessary condition that CFT correlators of ordinary CFT operators should obey the following property: the effects of quantum chaos, which become important in out of time order correlators (OTOC) at scrambling time, should be the same — to leading order at large N — in typical pure states as in the thermal ensemble
Summary
The black hole information paradox is a long-standing open problem, which is related to the smoothness of the black hole horizon [1, 2]. We provide evidence for the conjectured geometry of figure 1 for the onesided black hole, by perturbing the CFT Hamiltonian by the state-dependent operators O, in the schematic form δH = OO These perturbations allow particles that are localized in the left region of the geometry dual to a pure microstate, to traverse the black hole region and emerge in the right region and get directly detected by single-trace CFT operators. Other recent works which investigate the region behind the horizon of special, atypical pure states include [13,14,15,16,17]
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