Higher-order spin effects in the dynamics of compact binaries I. Equations of motion

TL;DR

This work computes the spin-orbit couplings of spinning compact binaries up to 2.5PN order within the post-Newtonian framework, including the full set of conserved Noetherian integrals and spin precession equations.Using the Dixon stress-energy tensor with a covariant spin supplementary condition, the authors derive the 2.5PN equations of motion in a general frame and specialize to the center-of-mass frame and quasi-circular orbits, providing explicit spin-orbit terms and consistency checks against prior results.A rigorous computation of the spin parts of the PN potentials, together with Hadamard regularization, yields complete expressions for the spin corrections to the metric and motion, enabling precise modeling of orbital phase evolution for gravitational-wave templates.The companion paper BBF06spin completes the program by evaluating multipole moments and radiation to produce actual waveform phasing, underpinning improved LIGO/Virgo/LISA data analysis.

Abstract

We derive the equations of motion of spinning compact binaries including the spin-orbit (SO) coupling terms one post-Newtonian (PN) order beyond the leading-order effect. For black holes maximally spinning this corresponds to 2.5PN order. Our result for the equations of motion essentially confirms the previous result by Tagoshi, Ohashi and Owen. We also compute the spin-orbit effects up to 2.5PN order in the conserved (Noetherian) integrals of motion, namely the energy, the total angular momentum, the linear momentum and the center-of-mass integral. We obtain the spin precession equations at 1PN order beyond the leading term, as well. Those results will be used in a future paper to derive the time evolution of the binary orbital phase, providing more accurate templates for LIGO-Virgo-LISA type interferometric detectors.