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We use an effective field theory (EFT) approach to calculate the next toleading order (NLO) gravitational spin-orbit interaction between two spinningcompact objects. The NLO spin-orbit interaction provides the mostcomputationally complex sector of the NLO spin effects, previously derivedwithin the EFT approach. In particular, it requires the inclusion ofnon-stationary cubic self-gravitational interaction, as well as theimplementation of a spin supplementary condition (SSC) at higher orders. TheEFT calculation is carried out in terms of the non-relativistic gravitationalfield parametrization, making the calculation more efficient with no need torely on automated computations, and illustrating the coupling hierarchy of thedifferent gravitational field components to the spin and mass sources. Finally,we show explicitly how to relate the EFT derived spin results to the canonicalresults obtained with the ADM Hamiltonian formalism. This is done usingnon-canonical transformations, required due to the implementation of covariantSSC, as well as canonical transformations at the level of the Hamiltonian, withno need to resort to the equations of motion or the Dirac brackets.

Next-to-leading order gravitational spin-orbit coupling in an effective field theory approach