Gravitational Spin-Orbit Hamiltonian at NNNLO in the post-Newtonian framework

TL;DR

This paper derives a highly accurate spin-orbit interaction Hamiltonian for binary compact objects up to third order in the post-Newtonian expansion, using effective field theory and advanced computational techniques.

Contribution

It provides the first calculation of the spin-orbit Hamiltonian at NNNLO in the post-Newtonian framework employing a diagrammatic EFT approach with three-loop integrals.

Findings

Derived gauge-invariant binding energy

Computed scattering angle in specific regimes

Eliminated non-physical divergences in Hamiltonian

Abstract

We present the result of the spin-orbit interaction Hamiltonian for binary systems of rotating compact objects with generic spins, up to NNNLO corrections within the post-Newtonian expansion. The calculation is performed by employing the effective field theory diagrammatic approach, and it involves Feynman integrals up to three loops, evaluated within the dimensional regularization scheme. We apply canonical transformations to eliminate the non-physical divergences and spurious logarithmic behaviours of the Hamiltonian, and use the latter to derive the gauge-invariant binding energy and the scattering angle, in special kinematic regimes.