Gravity/Ensemble Duality

TL;DR

This paper investigates the state paradox in gravitational calculations of Hawking radiation entropy, clarifies the applicability of holographic prescriptions, and suggests that averaging over ensembles resolves the paradox.

Contribution

It identifies the manifestation of the state paradox in various holographic settings and proposes ensemble averaging as a resolution.

Findings

The state paradox appears in standard and doubly-holographic models.

Different homology rules influence the manifestation of the paradox.

Ensemble averaging of gravitational path integrals resolves the paradox.

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.