Abstract:
I present a derivation of the secondorder gravitational selfforce for a small, compact, spherical body. Using the method of matched asymptotic expansions, in a buffer region outside the small body I construct a general solution to the secondorder Einstein field equations in the Lorenz gauge, subject only to the condition that the buffer region surrounds the body. This general solution contains all the necessary information, and is sufficiently accurate, to obtain the secondorder field globally via a puncture/effectivesource scheme. I then find the secondorder piece of the force governing the body's motion by matching the general solution to an 'inner expansion' in which the metric takes the form of the small body's spherical spacetime as perturbed by tidal fields.
