Next to leading order spin-orbit effects in the motion of inspiralling compact binaries

TL;DR

This paper calculates the next-to-leading order spin-orbit effects in inspiralling compact binaries using effective field theory, confirming previous results and establishing a canonical formalism for future gravitational wave modeling.

Contribution

It provides a detailed EFT-based calculation of NLO spin-orbit effects, demonstrating equivalence with prior results and clarifying the use of different spin supplementary conditions.

Findings

Confirmed equivalence with previous results by Faye et al.

Validated the use of Newton-Wigner SSC at the action level.

Laid groundwork for NLO spin contributions to energy flux and phase evolution.

Abstract

Using effective field theory (EFT) techniques we calculate the next-to-leading order (NLO) spin-orbit contributions to the gravitational potential of inspiralling compact binaries. We use the covariant spin supplementarity condition (SSC), and explicitly prove the equivalence with previous results by Faye et al. in arXiv:gr-qc/0605139. We also show that the direct application of the Newton-Wigner SSC at the level of the action leads to the correct dynamics using a canonical (Dirac) algebra. This paper then completes the calculation of the necessary spin dynamics within the EFT formalism that will be used in a separate paper to compute the spin contributions to the energy flux and phase evolution to NLO.