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

Guillaume Faye (1) , Luc Blanchet (1) , Alessandra Buonanno (1, 2, 3)

1 IAP - Institut d'Astrophysique de Paris
2 Maryland Center for Fundamental Physics & Joint Space-Science Center, Department of Physics
3 APC (UMR_7164) - AstroParticule et Cosmologie

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.

Mots clés: post-Newtonian approximation; equations of motion; equations of precession; spin; compact binaries; gravitational-wave sources

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]

Guillaume Faye, Luc Blanchet, Alessandra Buonanno. Higher-order spin effects in the dynamics of compact binaries I. Equations of motion. 2006. ⟨hal-00076742v1⟩