1201.5089 (Adam Pound)

Second-order gravitational self-force    [PDF]

Adam Pound

Using a rigorous method of matched asymptotic expansions, I derive the
equation of motion of a small, compact body in an external vacuum spacetime
through second order in the body's mass (neglecting effects of internal
structure). The motion is found to be geodesic in a certain locally defined
regular geometry satisfying Einstein's equation at second order. I provide a
practical scheme for numerically obtaining both the metric of that regular
geometry and the complete second-order metric perturbation produced by the
body.

View original: http://arxiv.org/abs/1201.5089