Point particles in general relativity: beyond linear perturbation theory
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 Blanchet and Damour's Hadamard regularization, opening new avenues to second-order self-force calculations in black hole binaries.
Related
- Linear Stability and a Turning Point Principle for Barotropic Liquid Stars with a Free Boundary in General Relativity
- Deep Learning Detection of Beyond-General-Relativity Deviations in Gravitational-Wave Signals: A Detection-Threshold Study with Real LIGO Noise
- Asymptotic flatness beyond General Relativity
- Deglobalising the fit: how to search for physics beyond vacuum General Relativity in LISA catalogues
- Fluid statics of a perfect-gas sphere with general relativity
BibTeX
@misc{musaeus2026point,
title = {{Point particles in general relativity: beyond linear perturbation theory}},
author = {Jørgen Musaeus and Adam Pound and Samuel D. Upton},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10521},
eprint = {2609.10521},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10521},
}
RIS
TY - UNPB
TI - Point particles in general relativity: beyond linear perturbation theory
AU - Jørgen Musaeus
AU - Adam Pound
AU - Samuel D. Upton
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.10521
UR - https://arxiv.org/abs/2609.10521
AB - 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 Blanchet and Damour's Hadamard regularization, opening new avenues to second-order self-force calculations in black hole binaries.
ER -