Half-solution to the two-body problem in General Relativity
Abstract
We show that the introduction of two worldline parameters defines a different approach to computations in the effective field theory approach to the two-body problem in General Relativity and present some preliminary evidence for a reduction in computational complexity. These parameters obey a polynomial equation whose perturbative expansion recovers an infinite series of diagrams. Futhermore, we show that our equations define an effective two-body horizon for interacting particles in General Relativity; in the circular orbit case, it corresponds to the smallest conceivable separation up to which the orbit can remain circular. We expect our results to simplify higher-order computations in the two-body problem, as well as to give insights on the nonperturbative properties of interacting binaries.
Cite
@article{arxiv.2003.03366,
title = {Half-solution to the two-body problem in General Relativity},
author = {Adrien Kuntz},
journal= {arXiv preprint arXiv:2003.03366},
year = {2020}
}
Comments
16 pages, 6 figures. More detailed version accepted in PRD