  We examine the response of an Unruh-DeWitt particle detector coupled to a
massless scalar field on the (3+1)-dimensional Schwarzschild spacetime, in the
Boulware, Hartle-Hawking and Unruh states, for static detectors and detectors
on circular geodesics, by primarily numerical methods. For the static detector,
the response in the Hartle-Hawking state exhibits the known thermality at the
local Hawking temperature, and the response in the Unruh state is thermal at
the local Hawking temperature in the limit of a large detector energy gap. For
the circular-geodesic detector, we find evidence of thermality in the limit of
a large energy gap for the Hartle-Hawking and Unruh states, at a temperature
that exceeds the Doppler-shifted local Hawing temperature. Detailed
quantitative comparisons between the three states are given. The response in
the Hartle-Hawking state is compared with the response in the Minkowski vacuum
and in the Minkowski thermal state for the corresponding Rindler, drifted
Rindler, and circularly accelerated trajectories. The analysis takes place
within first-order perturbation theory and relies in an essential way on
stationarity.
