Binary spinning black hole Hamiltonian in canonical center-of-mass and rest-frame coordinates through higher post-Newtonian order

TL;DR

This paper transforms existing binary black hole Hamiltonians into fully canonical center-of-mass and rest-frame variables up to higher post-Newtonian orders, ensuring Lorentz invariance consistency.

Contribution

It provides explicit generating functions for canonical variables and clarifies the relation between total momentum and center-of-mass velocity in binary black hole systems.

Findings

Hamiltonians are expressed in canonical variables up to higher post-Newtonian order.

Mixture terms align with Lorentz invariance requirements.

Explicit generating functions for canonical variables are derived.

Abstract

The recently constructed Hamiltonians for spinless binary black holes through third post-Newtonian order and for spinning ones through formal second post-Newtonian order, where the spins are counted of zero post-Newtonian order, are transformed into fully canonical center-of-mass and rest-frame variables. The mixture terms in the Hamiltonians between center-of-mass and rest-frame variables are in accordance with the relation between the total linear momentum and the center-of-mass velocity as demanded by global Lorentz invariance. The various generating functions for the center-of-mass and rest-frame canonical variables are explicitly given in terms of the single-particle canonical variables. The no-interaction theorem does not apply because the world-line condition of Lorentz covariant position variables is not imposed.