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

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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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Funding Information
  • Ministero dell'Università e della Ricerca
  • Università degli Studi di Perugia
  • European Research Council (GWSky–101167314)

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