Next-to-next-to-leading order post-Newtonian linear-in-spin binary Hamiltonians

TL;DR

This work derives the next-to-next-to-leading order spin-orbit and spin(1)-spin(2) Hamiltonians for binary compact objects within an extended ADM canonical framework. It develops a full matter-only Hamiltonian by solving the PN-expanded constraint equations and employing a Routhian approach to eliminate dynamical TT gravitational degrees of freedom, using near-zone wave equations and dimensional regularization to control ultraviolet behavior. The authors provide explicit NNLO Hamiltonians, transform them to center-of-mass form, and perform consistency checks via the approximate Poincaré algebra and a test-spin in Kerr spacetime. The results enhance gravitational-wave template accuracy for spinning binaries and lay groundwork for further high-order spin and radiative corrections in PN gravity.

Abstract

The next-to-next-to-leading order post-Newtonian spin-orbit and spin(1)-spin(2) Hamiltonians for binary compact objects in general relativity are derived. The Arnowitt-Deser-Misner canonical formalism and its generalization to spinning compact objects in general relativity are presented and a fully reduced matter-only Hamiltonian is obtained. Several simplifications using integrations by parts are discussed. Approximate solutions to the constraints and evolution equations of motion are provided. Technical details of the integration procedures are given including an analysis of the short-range behavior of the integrands around the sources. The Hamiltonian of a test-spin moving in a stationary Kerr spacetime is obtained by rather simple approach and used to check parts of the mentioned results. Kinematical consistency checks by using the global (post-Newtonian approximate) Poincaré algebra are applied. Along the way a self-contained overview for the computation of the 3PN ADM point-mass Hamiltonian is provided, too.