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.