  The "external" or "bulk" motion of extended bodies is studied in general
relativity. Compact material objects of essentially arbitrary shape, spin,
internal composition, and velocity are allowed as long as there is no direct
(non-gravitational) contact with other sources of stress-energy. Physically
reasonable linear and angular momenta are proposed for such bodies and exact
equations describing their evolution are derived. Changes in the momenta depend
on a certain "effective metric" that is closely related to a non-perturbative
generalization of the Detweiler-Whiting R-field originally introduced in the
self-force literature. If the effective metric inside a self-gravitating body
can be adequately approximated by an appropriate power series, the
instantaneous gravitational force and torque exerted on it is shown to be
identical to the force and torque exerted on an appropriate test body moving in
the effective metric. This result holds to all multipole orders. The only
instantaneous effect of a body's self-field is to finitely renormalize the
"bare" multipole moments of its stress-energy tensor. The MiSaTaQuWa expression
for the gravitational self-force is recovered as a simple application. A
gravitational self-torque is obtained as well. Lastly, it is shown that the
effective metric in which objects appear to move is approximately a solution to
the vacuum Einstein equation if the physical metric is an approximate solution
to Einstein's equation linearized about a vacuum background.
