Black Holes, Entanglement and Random Matrices

TL;DR

This paper challenges the idea that strong entanglement always implies a wormhole in AdS/CFT, proposing a random matrix model for gravity probes to clarify when spacetime connectivity occurs.

Contribution

It introduces a random matrix framework for low-energy gravity probes, linking entanglement strength to spectral properties rather than spacetime connectivity.

Findings

Strong entanglement does not necessarily imply a wormhole.

Large correlations can exist without a connected spacetime.

Spectral properties of probes determine spacetime connectedness.

Abstract

We provide evidence that strong quantum entanglement between Hilbert spaces does not generically create semiclassical wormholes between the corresponding geometric regions in the context of the AdS/CFT correspondence. We propose a description of low-energy gravity probes as random operators on the space of black hole states. We use this description to compute correlators between the entangled systems, and argue that a wormhole can only exist if correlations are large. Conversely, we also argue that large correlations can exist in the manifest absence of a Lorentzian wormhole. Thus the strength of the entanglement cannot generically diagnose spacetime connectedness, without information on the spectral properties of the probing operators. Our random matrix picture of probes also provides suggestive insights into the problem of "seeing behind a horizon".