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

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.

arXiv commenttranscription error in Eqs. (2.17) corrected

References in corpus (35)

• Gravitational Waves from Mergin Compact Binaries: How Accurately Can One Extract the Binary's Parameters from the Inspiral Waveform?
• Coalescing binary systems of compact objects to (post)$^{5/2}-Newtonian order. V. Spin Effects
• An Effective Field Theory of Gravity for Extended Objects
• A precise determination of angular momentum in the black hole candidate GRO J1655-40
• The Last Three Minutes: Issues in Gravitational Wave Measurements of Coalescing Compact Binaries
• Stellar disk in the galactic center -- a remnant of a dense accretion disk?
• Gravitational radiation from inspiralling compact binaries completed at the third post-Newtonian order
• Spin effects in the inspiral of coalescing compact binaries
• Improved filters for gravitational waves from inspiralling compact binaries
• Post-Newtonian corrections to the motion of spinning bodies in NRGR
• Detecting gravitational waves from precessing binaries of spinning compact objects: Adiabatic limit
• Gravitational-Wave Inspiral of Compact Binary Systems to 7/2 Post-Newtonian Order
• Higher-order spin effects in the dynamics of compact binaries II. Radiation field
• Black hole accretion discs: reality confronts theory
• Third post-Newtonian dynamics of compact binaries: Noetherian conserved quantities and equivalence between the harmonic-coordinate and ADM-Hamiltonian formalisms
• General relativistic dynamics of compact binaries at the third post-Newtonian order
• Parameter estimation of inspiralling compact binaries using 3.5 post-Newtonian gravitational wave phasing: The non-spinning case
• Gravitational field and equations of motion of compact binaries to 5/2 post-Newtonian order
• Third post-Newtonian dynamics of compact binaries: Equations of motion in the center-of-mass frame
• The 2.5PN gravitational wave polarisations from inspiralling compact binaries in circular orbits
• Detection template families for gravitational waves from the final stages of binary--black-hole inspirals: Nonspinning case
• Gravitational field and equations of motion of spinning compact binaries to 2.5 post-Newtonian order
• Hadamard Regularization
• Self-interaction spin effects in inspiralling compact binaries
• On the equations of motion of point-particle binaries at the third post-Newtonian order
• Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. III. Radiation reaction for binary systems with spinning bodies
• Gravitational waves from a spinning particle in circular orbits around a rotating black hole
• A physical template family for gravitational waves from precessing binaries of spinning compact objects: Application to single-spin binaries
• A quasi-physical family of gravity-wave templates for precessing binaries of spinning compact objects: Application to double-spin precessing binaries
• Post-Newtonian expansion of gravitational waves from a particle in circular orbit around a Schwarzschild black hole
• Lorentzian regularization and the problem of point-like particles in general relativity
• Spin-spin effects in radiating compact binaries
• Bounds on Expected Black Hole Spins in Inspiraling Binaries
• Detecting gravitational waves from precessing binaries of spinning compact objects. II. Search implementation for low-mass binaries
• Non-precessional spin-orbit effects on gravitational waves from inspiraling compact binaries to second post-Newtonian order

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