Entanglement generation outside a Schwarzschild black hole and the Hawking effect

TL;DR

This paper investigates how two atoms outside a Schwarzschild black hole become entangled due to Hawking radiation, analyzing different vacuum states and the influence of spacetime curvature on entanglement.

Contribution

It provides a detailed analysis of entanglement generation in a black hole spacetime for various vacua, highlighting the effects of backscattering and the horizon.

Findings

Atoms become entangled even if initially separable.

Backscattering affects entanglement only in the Unruh vacuum.

Entanglement persists away from the event horizon.

Abstract

We examine the Hawking effect by studying the asymptotic entanglement of two mutually independent two-level atoms placed at a fixed radial distance outside a Schwarzschild black hole in the framework of open quantum systems. We treat the two-atom system as an open quantum system in a bath of fluctuating quantized massless scalar fields in vacuum and calculate the concurrence, a measurement of entanglement, of the equilibrium state of the system at large times, for the Unruh, Hartle-Hawking and Boulware vacua respectively. We find, for all three vacuum cases, that the atoms turn out to be entangled even if they are initially in a separable state as long as the system is not placed right at the even horizon. Remarkably, only in the Unruh vacuum, will the asymptotic entanglement be affected by the backscattering of the thermal radiation off the space-time curvature. The effect of the back scatterings on the asymptotic entanglement cancels in the Hartle-Hawking vacuum case.