  The spontaneous excitation of a two-level atom held static outside a four
dimensional Schwarzschild black hole and in interaction with a massless scalar
field in the Boulware, Unruh and Hartle-Hawking vacuum is investigated and the
contributions of the vacuum fluctuations and radiation reaction to the rate of
change of the mean atomic energy are calculated separately. We find that for
the Boulware vacuum, the spontaneous excitation does not occur and the ground
state atoms are stable, while the spontaneous emission rate for excited atoms
in the Boulware vacuum, which is well-behaved at the event horizon, is not the
same as that in the usual Minkowski vacuum. However, both for the Unruh vacuum
and the Hartle-Hawking vacuum, our results show that the atom would
spontaneously excite, as if there were an outgoing thermal flux of radiation or
as if it were in a thermal bath of radiation at a proper temperature which
reduces to the Hawking temperature in the spatial asymptotic region, depending
on whether the scalar field is in the Unruh or Hartle-Hawking vacuum.
