Replica wormholes and the black hole interior

TL;DR

This paper demonstrates how replica wormholes explain the black hole information paradox by deriving the Page curve, analyzing topological replica geometries, and connecting these to entanglement wedge reconstruction.

Contribution

It provides a gravitational derivation of the Page curve using replica wormholes and explores their role in entanglement wedge reconstruction and ensemble averaging.

Findings

Replica wormholes reproduce the Page curve for black hole evaporation.

Topological replica geometries are crucial for understanding the Page transition.

Wormholes are linked to ensemble averaging in gravity theories.

Abstract

Recent work has shown how to obtain the Page curve of an evaporating black hole from holographic computations of entanglement entropy. We show how these computations can be justified using the replica trick, from geometries with a spacetime wormhole connecting the different replicas. In a simple model, we study the Page transition in detail by summing replica geometries with different topologies. We compute related quantities in less detail in more complicated models, including JT gravity coupled to conformal matter and the SYK model. Separately, we give a direct gravitational argument for entanglement wedge reconstruction using an explicit formula known as the Petz map; again, a spacetime wormhole plays an important role. We discuss an interpretation of the wormhole geometries as part of some ensemble average implicit in the gravity description.