Lensing of Vacuum Entanglement near Schwarzschild Black Holes

Abstract

An important feature of Schwarzschild spacetime is the presence of orbiting null geodesics and caustics. Their presence implies strong gravitational lensing effects for matter and radiation, i.e., for excitations of quantum fields. Here, we raise the question whether the lensing manifests itself also in the vacuum of quantum fields, namely by lensing the distribution of vacuum entanglement. To explore this possibility, we use the method of entanglement harvesting, where initially unentangled localized quantum systems are temporarily coupled to the field at different locations. We find that for the Boulware, Hartle-Hawking and Unruh vacua in 3+1 dimensional Schwarzschild spacetime, the harvesting of vacuum entanglement is indeed greatly amplified near caustics. In particular, we establish that pre-existing vacuum entanglement can be harvested also for lightlike separations.

arXiv comment22 pages (incl. 9 pages appendix), 10 figures (3 animated figures in ancillary files), RevTeX 4.1. v3: minor typos, update to published version

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• Gravitational entanglement witness through Einstein ring image
• The Unruh-DeWitt model and its joint interacting Hilbert space
• Harvesting Fermionic Field Entanglement in Schwarzschild Spacetime
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• Atom-field dynamics in curved spacetime
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• Entanglement and correlations between local observables in de Sitter spacetime
• A dynamic theory of entanglement for uniformly accelerated atoms
• Bipartite and tripartite entanglement in pure dephasing relativistic spin-boson model
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