On the interior geometry of a typical black hole microstate

TL;DR

The paper extends the Gao–Jafferis–Wall traversability framework to one-sided black holes dual to typical CFT states by employing state-dependent mirror operators and a double-trace perturbation. It shows that negative-energy shocks produced by V = O(0) tetilde{O}(0) can reveal behind-horizon physics via a CFT correlator, linking horizon smoothness to canonical-vs-typical state correlators at scrambling time. A central conjecture equates the one-sided and two-sided correlators in the large-N limit for low-frequency modes, supported by ETH-based arguments and SYK numerics, and it is extended to a Hayden–Preskill–like information-recovery protocol using mirror operators. Together, these results provide a concrete CFT realization of interior access for typical microstates and emphasize the role of state-dependent observables in black hole information transfer.

Abstract

We argue that the region behind the horizon of a one-sided black hole can be probed by an analogue of the double-trace deformation protocol of Gao-Jafferis-Wall. This is achieved via a deformation of the CFT Hamiltonian by a term of the form ${\cal O} \widetilde{\cal O}$, where $\widetilde{\cal O}$ denote the state-dependent "mirror operators". We argue that this deformation creates negative energy shockwaves in the bulk, which allow particles inside the horizon to escape and to get directly detected in the CFT. This provides evidence for the smoothness of the horizon of black holes dual to typical states. We argue that the mirror operators allow us to perform an analogue of the Hayden-Preskill decoding protocol. Our claims rely on a technical conjecture about the chaotic behavior of out-of-time-order correlators on typical pure states at scrambling time.

Figures (3)

• Figure 1: Conjectured Penrose diagram of a typical black hole microstate, to leading order in $1/N$, with a probe created by mirror operators (blue) and two negative energy shockwaves (orange).
• Figure 2: Numerics in SYK model for $N=24$. Left : $\langle \{\psi^I(t),\psi^J(0)\}^2\rangle$ in thermal (blue) and typical pure state (red). The scrambling time is designated by the vertical line. Right: diagonal matrix elements $\langle E_i| \{\psi^I(t),\psi^J(0)\}^2|E_i\rangle$ for $t\approx$ scrambling time. It shows slow variation with the energy, compatible with the ETH, within the dominant regions of the canonical ensemble (blue) and the microcanonical ensemble (red).
• Figure 3: A realization of the Hayden-Preskill protocol: the code subspace approximately factorizes into a tensor product corresponding to the algebras ${\cal A}$,${\cal A'}$. These tensor factors are entangled and provide the reservoir of EPR pairs needed to perform the teleportation. Here $U,\widetilde{U}$ is time evolution in the CFT and $V = {\cal O} \widetilde{\cal O}$ denotes the perturbation of the CFT Hamiltonian.