  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.
