Tensor networks for black hole interiors: non-isometries, quantum extremal surfaces, and wormholes

TL;DR

This paper develops hyperbolic tensor networks to model black hole interiors, exploring non-isometries, quantum extremal surfaces, and wormholes, providing insights into black hole information encoding and dynamics.

Contribution

It introduces a holographic tensor network model for black hole interiors that incorporates locality, dynamics, and encoding of interior states into radiation.

Findings

Tensor networks model black hole interiors with locality.

Quantum extremal surfaces evolve in evaporating black holes.

Wormhole descriptions connect interior states to radiation.

Abstract

We use hyperbolic tensor networks to construct a holographic map for black hole interiors that adds a notion of locality to the non-isometric codes proposed by Akers, Engelhardt, Harlow, Penington, and Vardhan. We use tools provided by these networks to study the relationship between non-isometries and quantum extremal surfaces behind the horizon. Furthermore, we introduce a limited notion of dynamics for these interior tensor networks based on the qudit models introduced by Akers et al., and study the evolution of quantum extremal surfaces in an evaporating black hole. We also find a tensor network description of a wormhole connecting the black hole interior to the radiation, providing a mechanism for interior states and operators to be encoded in the radiation after the Page time. As a particular case, we construct a tensor network realization of the backwards-forwards maps recently proposed to incorporate non-trivial effective dynamics in dynamical constructions of these non-isometric black hole codes.