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

TL;DR

This paper derives higher-order spin-orbit coupling equations of motion for compact binaries, confirming previous results and computing conserved quantities up to 2.5PN order, to improve gravitational wave templates.

Contribution

It provides the first derivation of spin-orbit effects at 2.5PN order in equations of motion and conserved quantities for spinning compact binaries.

Findings

Confirmed previous equations of motion with higher-order spin effects.

Computed conserved integrals up to 2.5PN order including spin-orbit terms.

Derived spin precession equations at 1PN order beyond leading.

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.