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Abstract

The "external" or "bulk" motion of extended bodies is studied in general relativity. Material objects of arbitrary shape, spin, internal composition, and velocity are allowed as long as the metric remains near a vacuum solution (with a possible cosmological constant). Under this restriction, physically reasonable linear and angular momenta are proposed that evolve as though they were the momenta of an extended test body moving in an effective vacuum metric. This result holds to all multipole orders. The portion of the physical metric that does not directly affect the motion is a slightly generalized form of the Detweiler-Whiting S-field originally introduced in the context of self-force. This serves only to (finitely) renormalize the "bare" multipole moments of the object's stress-energy tensor. The MiSaTaQu expression for the gravitational self-force is recovered as a simple application. A gravitational self-torque is obtained as well. Lastly, a certain exact result is derived that may provide a basis for understanding self-interaction at higher orders.