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arxiv: 1201.5089 · v2 · submitted 2012-01-24 · 🌀 gr-qc

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Second-order gravitational self-force

Adam Pound
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classification 🌀 gr-qc
keywords bodyequationgeometrymethodmetricmotionorderregular
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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.

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  1. All-order structure of static gravitational interactions and the seventh post-Newtonian potential

    hep-th 2026-04 unverdicted novelty 6.0

    A closed formula computes static post-Newtonian corrections at arbitrary odd orders in gravity, yielding the explicit seventh post-Newtonian potential that matches an independent diagrammatic method.