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Exploring the gauge flexibility of the linear-in-spin effective-one-body Hamiltonian at the 5.5 post-Newtonian order

Andrea Placidi1,*, Luca Sebastiani2,†, and Gianluca Grignani1,‡

  • *Contact author: andrea.placidi7@gmail.com
  • †Contact author: luca.sebastiani@aei.mpg.de
  • ‡Contact author: gianluca.grignani@unipg.it
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Phys. Rev. D 113, 084009 – Published 3 April, 2026

DOI: https://doi.org/10.1103/435y-8241

Abstract

We derive the gauge-general expressions of the two gyro-gravitomagnetic functions entering the spin-orbit sector of the effective-one-body (EOB) Hamiltonian up to the fifth-and-half post-Newtonian (5.5PN) order. Our results include both local and nonlocal-in-time contributions, providing the most general analytical formulation of the linear-in-spin conservative dynamics within the EOB framework. These expressions are then employed to compute two gauge-invariant observables for quasicircular orbits: the binding energy and the fractional periastron advance. We also use them to compare two spin gauge choices: the well-known Damour-Jaranowski-Schäfer (DJS) gauge, in which the gyro-gravitomagnetic functions are independent of the orbital angular momentum, and the alternative anti-DJS (or DJS¯) gauge, designed to reproduce in the test-mass limit the spin-orbit interaction of a spinning test particle in a Kerr background. For a circular, equal-mass, equal-spin binary, our analysis indicates that the DJS¯ gauge provides a slightly improved description of the inspiral dynamics, suggesting potential advantages for its use in future EOB waveform models.

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Phys. Rev. D 113, 084009– Published 3 April, 2026
  • Received 2 December 2025
  • Accepted 12 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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