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

TL;DR

This paper advances the theoretical modeling of spinning compact binaries by computing higher-order spin-orbit effects at 3.5PN order, refining the equations governing their motion and spin evolution, crucial for gravitational wave analysis.

Contribution

It derives the next-to-next-to-leading order spin-orbit terms in the equations of motion, spin evolution, and metric for compact binaries, and simplifies these in the center-of-mass frame for quasi-circular orbits.

Findings

Derived 3.5PN order spin-orbit correction terms.

Expressed results using conserved Euclidean spin variables.

Facilitates future gravitational-wave phase modeling.

Abstract

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.