  The gravitational field of a particle of small mass $\mu$ moving through
curved spacetime, with metric $g_{ab}$, is naturally and easily decomposed into
two parts each of which satisfies the perturbed Einstein equations through
$O(\mu)$. One part is an inhomogeneous field $h^S_{ab}$ which, near the
particle, looks like the Coulomb $\mu/r$ field with tidal distortion from the
local Riemann tensor. This singular field is defined in a neighborhood of the
small particle and does not depend upon boundary conditions or upon the
behavior of the source in either the past or the future. The other part is a
homogeneous field $h^R_{ab}$. In a perturbative analysis, the motion of the
particle is then best described as being a geodesic in the metric
$g_{ab}+h^R_{ab}$. This geodesic motion includes all of the effects which might
be called radiation reaction and conservative effects as well.
