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arXiv · 2609.10521

Point particles in general relativity: beyond linear perturbation theory

Jørgen Musaeus·Adam Pound·Samuel D. Upton
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Abstract

Point particles are generically ill defined in fully nonlinear general relativity, although they are naturally well defined in linear perturbation theory. In a previous paper, two of us showed how they can be rigorously defined from matched asymptotic expansions at second order in perturbation theory on a generic background spacetime. Here we show how the resulting field equations can be recast in a more practical, more fully ``skeletonized'' form. We also show that this form of the field equations enables simple derivations of equations of motion. Finally, we show how calculations in second-order perturbation theory can bypass the use of singular ``punctures'' and make rigorous use of off-the-shelf regularization methods such as Hadamard regularization, opening new avenues to second-order self-force calculations in black hole binaries.

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Jørgen Musaeus, Adam Pound, Samuel D. Upton. 2026-09-09. Point particles in general relativity: beyond linear perturbation theory. https://arxiv.org/abs/2609.10521

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