On the comparison of results regarding the post-Newtonian approximate treatment of the dynamics of extended spinning compact binaries

TL;DR

This paper reviews various Hamiltonians and potentials used in post-Newtonian modeling of spinning binary systems and introduces a method for direct comparison of these formulations at higher orders.

Contribution

It presents a new method for directly comparing conservative Hamiltonians and potentials in post-Newtonian dynamics up to the next-to-leading order.

Findings

Compiled a comprehensive review of existing Hamiltonians and potentials.

Developed a method for direct comparison at higher post-Newtonian orders.

Facilitates consistency checks among different formulations.

Abstract

A brief review is given of all the Hamiltonians and effective potentials calculated hitherto covering the post-Newtonian (pN) dynamics of a two body system. A method is presented to compare (conservative) reduced Hamiltonians with nonreduced potentials directly at least up to the next-to-leading-pN order.