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Wormholes from averaging over states

Ben Freivogel, Dora Nikolakopoulou, Antonio F. Rotundo

SciPost Phys. 14, 026 (2023) · published 1 March 2023


An important question about black holes is to what extent a typical pure state differs from the ensemble average. We show that this question can be answered within semi-classical gravity. We focus on the quantum deviation, which measures the fluctuations in the expectation value of an operator in an ensemble of pure states. For a large class of ensembles and observables, these fluctuations are calculated by a correlation function in the eternal black hole background, which can be reliably calculated within semi-classical gravity. This implements the idea of [arXiv:2002.02971] that wormholes can arise from averages over states rather than theories. As an application, we calculate the size of the long-time correlation function $\langle A(t) A(0)\rangle$.

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