# Probing typical black hole microstates

## TL;DR

This paper explores the geometry of typical black hole microstates in AdS/CFT, proposing that they include a spacelike region described by mirror operators, and investigates their chaotic properties and information retrieval protocols.

## Contribution

It introduces a framework using mirror operators to describe the extended geometry of typical black hole microstates and analyzes their chaotic behavior and information recovery mechanisms.

## Key findings

- Mirror operators can describe the spacelike region of typical microstates.
- Out-of-time-order correlators exhibit thermal chaos at scrambling time.
- Mirror operators enable an analogue of the Hayden-Preskill protocol.

## 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.