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

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 (2006 Phys. Rev. D 74 104033 (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.