The 6th Post-Newtonian Potential Terms at $O(G_N^4)$

TL;DR

This paper computes the 6th post-Newtonian order potential terms for binary systems at fourth order in Newton's constant, providing detailed calculations and comparisons with recent literature.

Contribution

It presents the explicit calculation of 6PN potential contributions at $O(G_N^4)$, advancing the precision of gravitational potential models for binary systems.

Findings

Derived the 6PN potential terms at $O(G_N^4)$ in harmonic coordinates.

Compared results with recent literature to validate calculations.

Enhanced the accuracy of post-Newtonian gravitational models.

Abstract

We calculate the potential contributions of the Hamiltonian in harmonic coordinates up 6PN for binary mass systems to $O(G_N^4)$ and perform comparisons to recent results in the literature \cite{Bern:2021dqo} and \cite{Bini:2020nsb}.