Two-body gravitational spin-orbit interaction at linear order in the mass ratio

Abstract

We analytically compute, to linear order in the mass-ratio, the "geodetic" spin precession frequency of a small spinning body orbiting a large (non-spinning) body to the eight-and-a-half post-Newtonian order, thereby extending previous analytical knowledge which was limited to the third post-Newtonian level. These results are obtained applying analytical gravitational self-force theory to the first-derivative level generalization of Detweiler's gauge-invariant redshift variable. We compare our analytic results with strong-field numerical data recently obtained by S.~R.~Dolan et al. [Phys.\ Rev.\ D {\bf 89}, 064011 (2014)]. Our new, high-post-Newtonian-order results capture the strong-field features exhibited by the numerical data. We argue that the spin-precession will diverge as $\approx -0.14/(1-3y)$ as the light-ring is approached. We transcribe our kinematical spin-precession results into a corresponding improved analytic knowledge of one of the two (gauge-invariant) effective gyro-gravitomagnetic ratios characterizing spin-orbit couplings within the effective-one-body formalism. We provide simple, accurate analytic fits both for spin-precession and the effective gyro-gravitomagnetic ratio. The latter fit predicts that the linear-in-mass-ratio correction to the gyro-gravitomagnetic ratio changes sign before reaching the light-ring. This strong-field prediction might be important for improving the analytic modeling of coalescing spinning binaries.

22 pages, 3 figures, revtex macros

References in corpus (12)

• Higher-order spin effects in the dynamics of compact binaries I. Equations of motion
• Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling
• Effective one body approach to the dynamics of two spinning black holes with next-to-leading order spin-orbit coupling
• Tidal effects in binary neutron star coalescence
• Improved effective-one-body description of coalescing nonspinning black-hole binaries and its numerical-relativity completion
• High-Order Post-Newtonian Fit of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry
• Next-to-next-to-leading order spin-orbit effects in the near-zone metric and precession equations of compact binaries
• Analytic modelling of tidal effects in the relativistic inspiral of binary neutron stars
• Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism
• Next-to-leading order gravitational spin-orbit coupling in an effective field theory approach
• ADM canonical formalism for gravitating spinning objects
• Analytic determination of the eight-and-a-half post-Newtonian self-force contributions to the two-body gravitational interaction potential

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• Gravitational spin-orbit coupling in binary systems, post-Minkowskian approximation and effective one-body theory
• Evolution of small-mass-ratio binaries with a spinning secondary
• Tidal invariants for compact binaries on quasi-circular orbits
• Comparison Between Self-Force and Post-Newtonian Dynamics: Beyond Circular Orbits
• Analytic determination of high-order post-Newtonian self-force contributions to gravitational spin precession
• Spin-orbit precession for eccentric black hole binaries at first order in the mass ratio
• Spin-orbit precession along eccentric orbits for extreme mass ratio black hole binaries and its effective-one-body transcription
• Linear-in-mass-ratio contribution to spin precession and tidal invariants in Schwarzschild spacetime at very high post-Newtonian order
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• Spin dynamics of a millisecond pulsar orbiting closely around a massive black hole
• Taming the post-Newtonian expansion: Simplifying the modes of the gravitational wave energy flux at infinity for a point particle in a circular orbit around a Schwarzschild black hole
• Tidal heating and torquing of the primary black hole in eccentric-orbit, non-spinning extreme-mass-ratio inspirals to 22PN order
• Post-Newtonian expansion of the spin-precession invariant for eccentric-orbit non-spinning extreme-mass-ratio inspirals to 9PN and $e^{16}$
• High-order post-Newtonian expansion of the redshift invariant for eccentric-orbit non-spinning extreme-mass-ratio inspirals
• Gyroscope precession along unbound equatorial plane orbits around a Kerr black hole
• Analytical solutions of bound timelike geodesic orbits in effective-one-body frame