SL (2, R) lattices as information processors

Abstract

Black holes past their Page times should act as efficient scramblers and information mirrors. The information of the infalling bits are rapidly encoded by the old black hole in the Hawking quanta, but it should take time that is exponential in the Page time entropy to decode the interior. Motivated by the features of fragmentation instability of near-extremal black holes, we construct a simple phenomenological model of the black hole as a lattice of interacting nearly AdS2 throats with gravitational hair charges propagating over the lattice. We study the microstate solutions and their response to shocks. The energy of the shocks are almost wholly absorbed by the total Arnowitt-Deser-Misner mass of the AdS2 throats, but the information of their locations and time ordering come out in the hair oscillations, which decouple from the final microstate to which the full system quickly relaxes. We discuss the Hayden-Preskill protocol of decoding infalling information. We also construct generalizations of our model involving a lattice of AdS2 throats networked via wormholes and their analogs in the form of tensor networks of Sachdev-Ye-Kitaev spin states.