Spin(1)Spin(2) Effects in the Motion of Inspiralling Compact Binaries at Third Order in the Post-Newtonian Expansion

TL;DR

This paper employs effective field theory to calculate third-order Post-Newtonian spin effects in binary systems, providing a canonical formalism that ensures consistency with previous results and enhances understanding of spin interactions in gravitational wave sources.

Contribution

It introduces a formalism that imposes the spin supplementarity condition in a canonical framework at all PN orders, extending previous results on spin effects in binary inspirals.

Findings

Derived spin-spin and spin-orbit potentials at 3PN order

Established equivalence with previous SSC-based results

Enhanced formalism for spin dynamics in compact binaries

Abstract

We use effective field theory techniques to compute the potentials due to spin-spin and spin-orbit effects, from which the spin(1)spin(2) contribution to the motion of spinning compact binaries to third Post-Newtonian (PN) order follow. We use a formalism which allows us to impose the spin supplementarity condition (SSC) in a canonical framework to all orders in the PN expansion. We explicitly show the equivalence with our previous results, obtained using the Newton-Wigner SSC at the level of the action for spin-spin and spin-orbit potentials reported in arXiv:gr-qc/0604099 and arXiv:0712.2032[gr-qc] respectively.