Black Holes, Entanglement and Random Matrices

TL;DR

This work questions whether entanglement generically implies a semiclassical wormhole in AdS/CFT, and introduces a random-matrix description of low-energy gravity probes to test this link. By treating bulk operators as Gaussian random matrices on the black hole microstate space, the authors show that typical entangled states yield two-sided correlators suppressed by a factor $e^{-S}$ relative to one-sided correlators, signaling the absence of a smooth ER bridge unless the entangled state is special (e.g., the identity-like coherence). Extending the framework to energy-changing ensembles reproduces quasinormal-mode decays and aligns with ETH-like structures, while highlighting differences between the canonical/microcanonical cases and generic pure states. The analysis also clarifies the confined phase, where structured operators in thermal AdS can produce large two-sided correlations without a Lorentzian wormhole, underscoring the crucial role of operator randomness for behind-horizon physics. Overall, the paper provides a coherent random-operator picture that captures universal correlator structure, affords analytic continuation beyond the horizon, and suggests a perturbative horizon dynamics compatible with random matrices, with implications for the ER=EPR program and black hole information questions.

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".