Probing typical black hole microstates

TL;DR

The paper proposes that the bulk dual of a typical AdS black hole microstate includes an extended exterior and a left interior region described by mirror operators, enabling a one-sided analogue of traversable wormholes through state-dependent CFT perturbations. It formalizes a code-subspace and a mirror-operator algebra, derives a necessary condition that typical-pure-state OTOCs match thermal scrambling behavior (consistent with ETH), and tests these ideas in the SYK model. It then develops a one-sided traversable protocol using $rak O$ and $ ilde{rak O}$ perturbations, analyzes energy and backreaction via shockwaves and gravitational Wilson lines, and presents thought experiments (including Hayden-Preskill-type decoding) illustrating information retrieval from behind the horizon. Collectively, the work provides a CFT framework for a smooth interior in typical black holes and connects interior geometry to observable CFT correlators and information-theoretic protocols.

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.

Figures (8)

• Figure 1: A proposal for the geometry dual to a typical black hole microstate.
• Figure 2: Perturbations of $H_{\rm CFT}$ by state-dependent operators can create negative energy shockwaves (yellow), which allow a probe from the left region (blue) to get detected by simple operators in the CFT.
• Figure 3: Left: AdS black hole formed by collapse. Right: conjectured bulk geometry of a typical black hole microstate in a single CFT. The left region makes sense up to a cut-off region (dotted lines) and there is no left CFT.
• Figure 4: An alternative to our proposal: typical states have a firewall on the horizon. This would be consistent with the Killing isometry, but would correspond to modifications of general relativity at low curvatures.
• Figure 5: Two different choices of localizing the mirror operators in physical time, corresponding to different identifications of physical time $t$ with the coordinate on the left region. The two diagrams correspond to different choices of $T$, the left diagram is for $T=0$. Notice that the bulk geometry of the left region, if it is defined relationally to the right boundary, is the same in both cases. However, the types of allowed active perturbations of the state are different.