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

TL;DR

This paper advances gravitational waveform modeling by deriving the spin-orbit coupling at 5.5PN order, combining self-force results with the effective-one-body formalism to improve accuracy in binary dynamics predictions.

Contribution

It provides the first derivation of 5.5PN spin-orbit coupling, integrating local and nonlocal effects with self-force data, enhancing waveform models for gravitational-wave analysis.

Findings

Derived 5.5PN spin-orbit coupling coefficients.

Incorporated results into effective-one-body models.

Improved agreement with numerical relativity data.

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, 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 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.