Spin-orbit precession for eccentric black hole binaries at first order in the mass ratio

Abstract

We consider spin-orbit ("geodetic") precession for a compact binary in strong-field gravity. Specifically, we compute $\psi$, the ratio of the accumulated spin-precession and orbital angles over one radial period, for a spinning compact body of mass $m_1$ and spin $s_1$, with $s_1\ll G{m}_1^2/c$, orbiting a non-rotating black hole. We show that $\psi$ can be computed for eccentric orbits in both the gravitational self-force and post-Newtonian frameworks, and that the results appear to be consistent. We present a post-Newtonian expansion for $\psi$ at next-to-next-to-leading order, and a Lorenz-gauge gravitational self-force calculation for $\psi$ at first order in the mass ratio. The latter provides new numerical data in the strong-field regime to inform the Effective One-Body model of the gravitational two-body problem. We conclude that $\psi$ complements the Detweiler redshift $z$ as a key invariant quantity characterizing eccentric orbits in the gravitational two-body problem.

Matches the published version in CQG

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Cited by in corpus (6)

• Evolution of small-mass-ratio binaries with a spinning secondary
• Self-Force Calculations with a Spinning Secondary
• Spin-orbit precession along eccentric orbits for extreme mass ratio black hole binaries and its effective-one-body transcription
• Relativistic effects due to gravimagnetic moment of a rotating body
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• High-order post-Newtonian expansion of the generalized redshift invariant for eccentric-orbit, equatorial extreme-mass-ratio inspirals with a spinning primary