Gravity/Ensemble Duality

Abstract

For the first time, a gravitational calculation was recently shown to yield the Page curve for the entropy of Hawking radiation, consistent with unitary evolution. However, the calculation takes as essential input Hawking's result that the radiation entropy becomes large at late times. We call this apparent contradiction the state paradox. We exhibit its manifestations in standard and doubly-holographic settings, with and without an external bath. We clarify which version(s) of the Ryu-Takayanagi prescription apply in each setting. We show that the two possible homology rules in the presence of a braneworld generate a bulk dual of the state paradox. The paradox is resolved if the gravitational path integral computes averaged quantities in a suitable ensemble of unitary theories, a possibility supported independently by several recent developments.

43 pages, 12 figures, v2: references added, v3: published version, various minor improvements

References in corpus (8)

• Holographic representation of local bulk operators
• JT gravity as a matrix integral
• Page Curve for an Evaporating Black Hole
• Islands in Asymptotically Flat 2D Gravity
• Black hole entropy as entanglement entropy: a holographic derivation
• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity
• Pure states in the SYK model and nearly-$Ad{S}_2$ gravity
• The Black Hole Information Problem

Cited by in corpus (2)

• More quantum noise from wormholes
• Replica wormhole and island incompatibility with monogamy of entanglement