Probing typical black hole microstates

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 perturbations 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.

Information transfer and black hole evaporation via traversable BTZ wormholes

“…Then, if the collapsing shell is sent into the bulk at a time not much later than at which the diary was lost, the diary will be trapped in the newly formed black hole. However, Bob could send a negative energy shockwave into the bulk, perhaps by introducing a non-local coupling in the spirit of [32], such that the diary could be retrieved from the black hole before it hits the singularity. The mechanism underlying this retrieval is of course again the traversable wormhole protocol.…”

Phases of scrambling in eigenstates

“…Statements of the kind (1.4) are intimately related to a number of recent developments surrounding the holographic understanding of black holes and their microstates and attempts to address the firewall paradox raised in [27]. For example the authors of [28] point out that if statements of the type (1.4) & (1.5) hold for typical states, then a typical microstate of a black hole itself contains information about behind-the-horizon physics. Our results hold for eigenstates and will thus extend to typical states that are superpositions of eigenstates in a small energy window as required by [28].…”

Eigenstate thermalization hypothesis and approximate quantum error correction

“…chaos, such as the decay of out-of-time-order correlators (OTOC) and operator growth, to quantum error correction [38][39][40][41][42][43][44]. By extension, we can then apply such results to understanding holographic CFTs and their duals, as part of a general program of applying tools and concepts from quantum information and error correction to understanding quantum gravity.…”