$SL(2,R)$ lattices as information processors

TL;DR

This paper models black holes as lattices of interacting $AdS_2$ throats to explore information encoding, scrambling, and decoding, connecting gravitational dynamics with quantum information protocols.

Contribution

It introduces a phenomenological lattice model of black holes with $AdS_2$ throats and analyzes their microstates, shock responses, and information decoding mechanisms.

Findings

Information of infalling bits is encoded in hair oscillations.

Shocks are absorbed with information about their origin and timing.

Model generalizes to wormhole networks and tensor network analogues.

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 $AdS_2$ 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 ADM mass of the $AdS_2$ 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 $AdS_2$ throats networked via wormholes and their analogues in the form of tensor networks of SYK spin-states.