Non-uniqueness of the third post-Newtonian binary point-mass dynamics

TL;DR

This paper reveals that the non-uniqueness in third post-Newtonian binary dynamics stems from the choice of ADM-coordinate conditions, impacting the Hamiltonian formulation at this approximation level.

Contribution

It identifies the source of non-uniqueness in third post-Newtonian binary dynamics as related to coordinate condition choices.

Findings

Non-uniqueness linked to ADM-coordinate conditions

Implications for Hamiltonian formulations at 3PN order

Highlights coordinate dependence in post-Newtonian approximations

Abstract

It is shown that the recently found non-uniqueness of the third post-Newtonian binary point-mass ADM-Hamiltonian is related to the non-uniqueness at the third post-Newtonian approximation of the applied ADM-coordinate conditions.