# Wormholes from Averaging over States

### Submission summary

 As Contributors: Antonio Rotundo Arxiv Link: https://arxiv.org/abs/2105.12771v2 (pdf) Date accepted: 2022-05-17 Date submitted: 2022-02-22 15:29 Submitted by: Rotundo, Antonio Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory Approach: Theoretical

### Abstract

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 $\langle A(t) A(0)\rangle$.

###### Current status:
Publication decision taken: accept

Editorial decision: For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)

### List of changes

- Added paragraph at the end of the introduction (page 3) to clarify that the wormhole we find is Lorentzian;
- Corrected discussion of thermodynamic limit (second paragraph at beginning of sec. 3.1, page 10);
- Added one bullet point about polynomial tails to the discussion (last paragraph of conclusion at page 30);
- Added a sentence about higher order terms in G below eq. 6.19;
- Explicit reference to eq. 4.1 (above eq. 4.2);
- Rearranged discussion of purity (page 7 from eq. 2.23 to the end of sec. 2.1);
- Replace g with h in eq. 3.19;
- Swapped left and right basis states in eq. 3.6, 4.15, and 4.22;
- Added Theta in eq. 4.14;
- Changed notation for partial transpose in eq. 4.14, and 3.7;
- Added a footnote at page 8 clarifying some aspects of the partial transpose.