Gravitational spin-orbit and aligned spin$_1$-spin$_2$ couplings through third-subleading post-Newtonian orders

TL;DR

This paper advances the understanding of relativistic two-body dynamics by deriving high-order post-Newtonian spin couplings using scattering and self-force methods, and validates these results through numerical relativity comparisons.

Contribution

It provides the third-subleading (4.5PN and 5PN) spin-orbit and spin$_1$-spin$_2$ couplings for aligned spins, integrating these into an effective-one-body model.

Findings

Derived 4.5PN spin-orbit coupling for generic spins.

Derived 5PN spin$_1$-spin$_2$ coupling for aligned spins.

Improved EOB model accuracy confirmed by numerical relativity.

Abstract

The study of scattering encounters continues to provide new insights into the general relativistic two-body problem. The local-in-time conservative dynamics of an aligned-spin binary, for both unbound and bound orbits, is fully encoded in the gauge-invariant scattering-angle function, which is most naturally expressed in a post-Minkowskian (PM) expansion, and which exhibits a remarkably simple dependence on the masses of the two bodies (in terms of appropriate geometric variables). This dependence links the PM and small-mass-ratio approximations, allowing gravitational self-force results to determine new post-Newtonian (PN) information to all orders in the mass ratio. In this paper, we exploit this interplay between relativistic scattering and self-force theory to obtain the third-subleading (4.5PN) spin-orbit dynamics for generic spins, and the third-subleading (5PN) spin$_1$-spin$_2$ dynamics for aligned spins. We further implement these novel PN results in an effective-one-body framework, and demonstrate the improvement in accuracy by comparing against numerical-relativity simulations.