Black holes, entanglement and random matrices

Balasubramanian, Vijay; Berkooz, Micha; Ross, Simon F.; Simón, Joan

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'.

Citation

Balasubramanian, V., Berkooz, M., Ross, S. F., & Simón, J. (2014). Black holes, entanglement and random matrices. Classical and Quantum Gravity, 31(18), https://doi.org/10.1088/0264-9381/31/18/185009

• Journal Article Type: Article
• Online Publication Date: Aug 28, 2014
• Publication Date: Sep 1, 2014
• Deposit Date: Aug 29, 2014
• Publicly Available Date: Sep 3, 2014
• Journal: Classical and Quantum Gravity
• Print ISSN: 0264-9381
• Electronic ISSN: 1361-6382
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 31
• Issue: 18
• DOI: https://doi.org/10.1088/0264-9381/31/18/185009
• Public URL: https://durham-repository.worktribe.com/output/1454898