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We compute spin-orbit effects in the equations of motion, binding energy andenergy loss of binary systems of compact objects at the next-to-leading orderin the post-Newtonian (PN) approximation in the effective field theory (EFT)framework. We then use these quantities to compute the evolution of the orbitalfrequency and accumulated orbital phase including spin-orbit effects beyond thedominant order. To obtain the results presented in this paper, we make use ofknown ingredients in the EFT literature, such as the potential and themultipole moments with spin effects at next-to-leading order, and which aregiven in the linearized harmonic gauge and with the spins in the locally flatframe. We also obtain the correction to the center-of-mass frame caused byspin-orbit effects at next-to-leading order. We demonstrate the equivalencebetween our EFT results and those which were obtained elsewhere using differentformalisms. The results presented in this paper provide us with the finalingredients for the construction of theoretical templates for gravitationalwaves including next-to-leading order spin-orbit effects, which will bepresented in a future publication.

physical review. d/physical review. d.

Next-to-leading order spin-orbit effects in the equations of motion,  energy loss and phase evolution of binaries of compact bodies in the  effective field theory approach