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

TL;DR

This paper derives the most general gauge-dependent expressions for the spin-orbit sector of the EOB Hamiltonian at 5.5PN order, compares two gauge choices, and finds the anti-DJS gauge offers a slight improvement for equal-mass, equal-spin binaries.

Contribution

It provides the first comprehensive 5.5PN order gauge-general formulation of the linear-in-spin EOB Hamiltonian, including local and nonlocal contributions, and compares gauge choices for better modeling.

Findings

The anti-DJS gauge slightly improves the description of inspiral dynamics.

Derived gauge-general expressions for spin-orbit interactions at 5.5PN order.

Compared two gauge choices and identified potential advantages for waveform modeling.

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-Sch\"afer ($\rm DJS$) 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.