Canonical formulation of gravitating spinning objects at 3.5 post-Newtonian order

TL;DR

This paper extends the canonical formalism to include spinning objects at 3.5PN order, deriving a Hamiltonian and analyzing gravitational wave energy flux with agreement to Einstein equations.

Contribution

It introduces a canonical formalism for spinning gravitating objects at 3.5PN order, including a general interaction Hamiltonian and wave equation analysis.

Findings

Derived a 3.5PN order interaction Hamiltonian for spinning objects.

Confirmed agreement with Einstein equations for the wave equation.

Computed the energy flux at the spin-orbit level.

Abstract

The 3.5 post-Newtonian (PN) order is tackled by extending the canonical formalism of Arnowitt, Deser, and Misner to spinning objects. This extension is constructed order by order in the PN setting by utilizing the global Poincare invariance as the important consistency condition. The formalism is valid to linear order in the single spin variables. Agreement with a recent action approach is found. A general formula for the interaction Hamiltonian between matter and transverse-traceless part of the metric at 3.5PN is derived. The wave equation resulting from this Hamiltonian is considered in the case of the constructed formalism for spinning objects. Agreement with the Einstein equations is found in this case. The energy flux at the spin-orbit level is computed.