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

TL;DR

This paper derives a next-to-leading order Hamiltonian for the gravitational spin(1)-spin(2) interaction using ADM formalism, providing a new analytical tool for understanding binary systems with spinning bodies.

Contribution

It presents the first derivation of the next-to-leading order spin(1)-spin(2) Hamiltonian within the ADM canonical formalism.

Findings

Derived the next-to-leading order spin(1)-spin(2) Hamiltonian.

Compared results with other methods.

Provides a new analytical framework for spinning binary systems.

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.