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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 Placidi, Luca Sebastiani, Gianluca Grignani

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 quasi-circular 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 ($\rm DJS$) gauge, in which the gyro-gravitomagnetic functions are independent of the orbital angular momentum, and the alternative anti-$\rm DJS$ (or $\overline{\rm DJS}$) 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 $\overline{\rm DJS}$ gauge provides a slightly improved description of the inspiral dynamics, suggesting potential advantages for its use in future EOB waveform models.

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

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 quasi-circular 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 () gauge, in which the gyro-gravitomagnetic functions are independent of the orbital angular momentum, and the alternative anti- (or ) 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 gauge provides a slightly improved description of the inspiral dynamics, suggesting potential advantages for its use in future EOB waveform models.

Paper Structure

This paper contains 16 sections, 51 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Computational setup
  3. Nonlocal spin–orbit dynamics in full gauge generality at 5.5PN
  4. Delaunay-averaged nonlocal Hamiltonian at 5.5PN
  5. Nonlocal Delaunay-averaged EOB Hamiltonian at 5.5PN
  6. Nonlocal gyro-gravitomagnetic functions in full gauge generality at 5.5PN
  7. Local spin-orbit dynamics in full gauge generality at 5.5PN
  8. Conservative scattering angle: 5.5PN linear-in-spin terms
  9. Local gyro-gravitomagnetic functions in full gauge generality at 5.5PN
  10. Analytical consistency checks: Gauge invariant quantities
  11. Gauge flexibility of the gyro-gravitomagnetic functions
  12. The DJS spin gauge
  13. The $\overline{\rm DJS}$ spin gauge
  14. Performance comparison: binding energy in the DJS and $\overline{\text{DJS}}$ spin gauges
  15. Conclusions
  16. ...and 1 more sections

Figures (2)

  • Figure 1: Spin–orbit contribution to the binding energy for circular orbits as a function of $v_\omega$, shown in the DJS (left panel) and $\overline{\rm DJS}$ (right panel) spin gauges. In each panel, the numerical curve from Ref. Ossokine_2018 is displayed as a black dashed line, together with the analytical curves obtained by truncating the spin–orbit sector of the EOB Hamiltonian at different PN orders (see the legend in the insets). At 5.5PN order, the $\mathsf{X}^{\nu^2}_{59}=0$ curve is accompanied by a shaded band indicating the variation induced by changing $\mathsf{X}^{\nu^2}_{59}$ within the range $[-750,750]$. The upper edge of the shaded region corresponds to $\mathsf{X}^{\nu^2}_{59}=750$, while decreasing $\mathsf{X}^{\nu^2}_{59}$ produces a systematic downward shift of the curves, with the lower edge reached at $\mathsf{X}^{\nu^2}_{59}=-750$.
  • Figure 2: Direct comparison between the 5.5PN curves shown in Fig. \ref{['fig:singlegauges']} for the two spin gauges. To better emphasize the differences between the gauges, the range of $v_\omega$ displayed here is shorter than in Fig. \ref{['fig:singlegauges']}.