  We study the Hawking effect in terms of the geometric phase acquired by a
two-level atom as a result of coupling to vacuum fluctuations outside a
Schwarzschild black hole in a gedanken experiment. We treat the atom in
interaction with a bath of fluctuating quantized massless scalar fields as an
open quantum system, whose dynamics is governed by a master equation obtained
by tracing over the field degrees of freedom. The nonunitary effects of this
system are examined by analyzing the geometric phase for the Boulware, Unruh
and Hartle-Hawking vacua respectively. We find, for all the three cases, that
the geometric phase of the atom turns out to be affected by the space-time
curvature which backscatters the vacuum field modes. In both the Unruh and
Hartle-Hawking vacua, the geometric phase exhibits similar behaviors as if
there were thermal radiation at the Hawking temperature from the black hole.
So, a measurement of the change of the geometric phase as opposed to that in a
flat space-time can in principle reveal the existence of the Hawking radiation.
