Second-order gravitational self-force
General Relativity and Quantum Cosmology
2012-09-05 v2
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 outline a method of numerically obtaining both the metric of that regular geometry and the complete second-order metric perturbation produced by the body.
Cite
@article{arxiv.1201.5089,
title = {Second-order gravitational self-force},
author = {Adam Pound},
journal= {arXiv preprint arXiv:1201.5089},
year = {2012}
}
Comments
5 pages, added clarifications in response to referee comments, accepted for publication in PRL