  We study, by separately calculating the contributions of vacuum fluctuations
and radiation reaction to the atomic energy level shift, the Lamb shift of a
static two-level atom interacting with real massless scalar fields in the
Boulware, Unruh and Hartle-Hawking vacuums outside a Schwarzschild black hole.
We find that in the Boulware vacuum, the Lamb shift gets a correction arising
as a result of the backscattering of vacuum field modes off the space-time
curvature, which is reminiscent of the correction to the Lamb shift induced by
the presence of cavities. However, when the Unruh and Hartle-Hawking vacua are
concerned, our results show that the Lamb shift behaves as if the atom were
irradiated by a thermal radiation or immersed in a thermal bath at the Hawking
temperature, depending on whether the scalar field is in the Unruh or the
Hartle-Hawking vacuum. Remarkably, the thermal radiation is always
backscattered by the space-time geometry.
