Authors: Adam Pound
Date: 24 Jan 2012
Abstract: 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.
© M. Vallisneri 2012 — last modified on 2010/01/29
Tantum in modicis, quantum in maximis