Replica wormholes and the black hole interior

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.

Automated summary

Recent work has shown how to obtain the Page curve of an evaporating black hole through holographic computations of entanglement entropy. The validity of these computations is justified using the replica trick and geometries with a spacetime wormhole connecting the different replicas. The Page transition is studied in detail in a simple model by summing replica geometries with different topologies. Related quantities are computed in less detail in more complicated models like JT gravity coupled to conformal matter and the SYK model. Additionally, a direct gravitational argument for entanglement wedge reconstruction is given using the explicit formula known as the Petz map, where the spacetime wormhole plays a significant role. The interpretation of the wormhole geometries as part of some ensemble average implicit in the gravity description is also discussed.