The next-to-leading order gravitational spin(1)-spin(2) dynamics in Hamiltonian form

TL;DR

The paper delivers the first complete next-to-leading order spin(1)-spin(2) Hamiltonian for gravitational two-body dynamics within the ADM formalism using ADMTT coordinates. It presents two consistent derivations and confirms the result by constructing the global Poincaré algebra, including the center-of-mass generator that incorporates spin contributions. A key contribution is showing that full agreement with other approaches (e.g., Porto–Rothstein) requires including spin–orbit effects at this order, resolving prior inconsistencies. The work provides a rigorous, canonical-framework validation of the NLO spin-spin interaction with potential implications for high-precision modeling of spinning compact binaries and gravitational-wave physics.

Abstract

Based on recent developments by the authors a next-to-leading order spin(1)-spin(2) Hamiltonian is derived for the first time. The result is obtained within the canonical formalism of Arnowitt, Deser, and Misner (ADM) utilizing their generalized isotropic coordinates. A comparison with other methods is given.