Next-to-next-to-leading order spin-orbit effects in the near-zone metric and precession equations of compact binaries

Understand

We extend our previous work devoted to the computation of the next-to-next-to-leading order spin-orbit correction (corresponding to 3.5PN order) in the equations of motion of spinning compact binaries, by: (i) Deriving the corresponding spin-orbit terms in the evolution equations for the spins, the conserved integrals of the motion and the metric regularized at the location of the particles (obtaining also the metric all-over the near zone but with some lower precision); (ii) Performing the orbital reduction of the precession equations, near-zone metric and conserved integrals to the center- of-mass frame and then further assuming quasi-circular orbits (neglecting gravitational radiation reaction).

• The results are systematically expressed in terms of the spin variables with conserved Euclidean norm instead of the original antisymmetric spin tensors of the pole-dipole formalism.
• This work paves the way to the future computation of the next-to-next-to-leading order spin-orbit terms in the gravitational-wave phasing of spinning compact binaries.