English

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.

Keywords

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

R2 v1 2026-06-21T20:09:10.059Z