  For a particle in orbit about a static spherically symmetric body, we study
the change in self-force that results when the central body type (i.e., the
choice of interior metric for the Schwarzschild exterior) is changed. While a
straight self-force is difficult to compute because of the need for
regularization, such a "self-force difference" may be computed directly from
the mode functions of the relevant wave equations. This technique gives a
simple probe of the (non)locality of the force, as well as offers the practical
benefit of an easy determination of the self-force on a body orbiting an
arbitrary (static spherically symmetric) central body, once the corresponding
result for a black hole (or some other reference interior) is known. We derive
a general expression for the self-force difference at the level of a mode-sum
in the case of a (possibly non-minimally coupled) scalar charge and indicate
the generalization to the electromagnetic and gravitational cases. We then
consider specific choices of orbit and/or central body. Our main findings are:
(1) For charges held static at a large distance from the central body, the
self-force is independent of the central body type in the minimally coupled
scalar case and the electromagnetic case (but dependent in the nonminimally
coupled scalar case); (2) For circular orbits about a thin-shell spacetime in
the scalar case, the fractional change in self-force from a black hole
spacetime is much larger for the radial (conservative) force than for the
angular (dissipative) force; and (3) the radial self-force difference (between
these spacetimes) agrees closely for a static charge and a circular orbit of
the same radius.
