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Gravitational spin-orbit dynamics at the fifth-and-a-half post-Newtonian order

Mohammed Khalil*

  • Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, Potsdam 14476, Germany and Department of Physics, University of Maryland, College Park, Maryland 20742, USA

  • *mohammed.khalil@aei.mpg.de
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Phys. Rev. D 104, 124015 – Published 3 December, 2021

DOI: https://doi.org/10.1103/PhysRevD.104.124015

Abstract

Accurate waveform models are crucial for gravitational-wave data analysis, and since spin has a significant effect on the binary dynamics, it is important to improve the spin description in these models. In this paper, we derive the spin-orbit (SO) coupling at the fifth-and-a-half post-Newtonian (5.5PN) order. The method we use splits the conservative dynamics into local and nonlocal-in-time parts, and then relates the local-in-time part to gravitational self-force results by exploiting the simple mass-ratio dependence of the post-Minkowskian expansion of the scattering angle. We calculate the nonlocal contribution to the 5.5PN SO dynamics to eighth order in the small-eccentricity expansion for bound orbits, and to leading order in the large-eccentricity expansion for unbound orbits. For the local contribution, we obtain all of the 5.5PN SO coefficients from first-order self-force results for the redshift and spin-precession invariants, except for one unknown that could be fixed in the future by second-order self-force results. However, by incorporating our 5.5PN results in the effective-one-body formalism and comparing its binding energy to numerical relativity, we find that the remaining unknown has a small effect on the SO dynamics, demonstrating an improvement in accuracy at that order.

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Phys. Rev. D 104, 124015– Published 3 December, 2021
  • Received 27 October 2021
  • Accepted 3 November 2021
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