Replica Wormholes and Quantum Hair

https://arxiv.org/abs/2404.02331

Xavier Calmet, Stephen D.H. Hsu

We discuss recent applications of Euclidean path integrals to the black hole information problem. In calculations with replica wormholes as the next-to-leading order correction to the Gibbons-Hawking saddlepoint, the radiation density matrix approaches a pure state at late times, following the Page curve. We compare unitary evaporation of black holes (in real time), mediated by calculable quantum hair effects, with the replica wormhole results. Both replica wormhole and quantum hair approaches imply that radiation states are macroscopic superpositions of spacetime backgrounds, invalidating firewall and monogamy of entanglement constructions. Importantly, identification of modes inside the horizon with radiation modes (i.e., large scale nonlocality across the horizon) is not required to provide a physical picture of unitary evaporation. Radiation modes can encode the interior information while still remaining independent degrees of freedom.

Wormholes dominate the Gibbons-Hawking saddlepoint of the Euclidean path integral after the Page time. This is because wormholes can connect the interiors of any two black holes i,j. At late times the number of such pairs grows as the dimensionality of the radiation Hilbert space squared.

The wormholes connect BHs with macroscopically different recoil trajectories. This means the radiation approaches a pure state that is a macroscopic superposition - very similar to what our quantum hair expressions indicate.

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