Second-order gravitational self-force

Details Second-order gravitational self-force Second-order gravitational self-force

2012-01-24

arxiv.org/abs/1201.5089v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

5 pages, submitted to PRL

Scientific paper

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.

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