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

2016/08/31 by Sarp Akçay, Sarp Akcay, David Dempsey +2 · 2 citations
Physics and Astronomy · #Astrophysical Phenomena and Observations #Astrophysics #Binary black hole #Black hole (networking) #Circular orbit #Classical mechanics #Gamma-ray bursts and supernovae #Gravitation #Gravitational field #Gravitational potential #Gravitational wave #Mass ratio #Orbit (dynamics) #Physics #Precession #Pulsars and Gravitational Waves Research #Quantum mechanics #Spin (aerodynamics) #gr-qc

paper · pdf · doi:10.1088/1361-6382/aa61d6

published as Classical and Quantum Gravity, Volume 34, Number 8, 084001, 2017 · Matches the published version in CQG

openalex publication_date 2017/03/20 · arxiv created 2017/03/30 · arxiv updated 2017/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Abstract We consider spin–orbit (‘geodetic’) precession for a compact binary in strong-field gravity. Specifically, we compute ψ , 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mstyle displaystyle="false"> <mml:msub> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> <mml:mn>1</mml:mn> </mml:msub> </mml:mstyle> <mml:mo>≪</mml:mo> <mml:mi>G</mml:mi> <mml:mstyle displaystyle="false"> <mml:msubsup> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mstyle> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>c</mml:mi> </mml:mstyle> </mml:math> , orbiting a non-rotating black hole. We show that ψ 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 ψ at next-to-next-to-leading order, and a Lorenz-gauge gravitational self-force calculation for ψ 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 ψ complements the Detweiler redshift z as a key invariant quantity characterizing eccentric orbits in the gravitational two-body problem.

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