Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Musaeus, Jørgen, Pound, Adam, Upton, Samuel D.
Institution: University of Southampton
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: UK Research and Innovation
Award: G6171340896
OpenAlex ID: W7212185500