On the interior geometry of a typical black hole microstate

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 O O, where 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.

Complexity and typical microstates

“…This is certainly possible; particularly for the action one can imagine getting such a divergent contribution (although divergences in the action for the bulk description of individual microstates could be problematic for other arguments, for example about tunneling rates [26]). However, it is encouraging that the geometric description for typical states proposed in [8,9] naturally produces such a divergence, in a way which is consistent with our heuristic ideas about the relation of complexity to the growth of the wormhole geometry in the spacetime.…”

An infalling observer and behind the horizon cutoff

“…In this case one could still get a cutoff behind the horizon though its value at leading order is grater than the previous one by a factor of 2 2 d+1 . This situation might be thought of as the case in which the corresponding solution represents a typical black hole microstates of which the gravitational dual is provided by an eternal black hole when only a portion of the left asymptotic region is taken into account [23]. Therefore we are left with a CFT at the boundary of the right exterior side and the left side is capped by a cutoff.…”

Probing typical black hole microstates

“…Part of the results of this paper were reported in a shorter note [12]. Other recent works which investigate the region behind the horizon of special, atypical pure states include [13,14,15,16,17].…”