The binary black-hole dynamics at the third post-Newtonian order in the orbital motion

TL;DR

This paper investigates the complex orbital dynamics of binary black holes at the third post-Newtonian order, highlighting ambiguities related to static and kinetic aspects and their implications for Lorentz invariance.

Contribution

It clarifies the static and kinetic ambiguities in third post-Newtonian binary black-hole dynamics and discusses their relation to initial value solutions and Lorentz invariance.

Findings

Static ambiguity linked to different initial value solutions.

Kinetic ambiguity affects the relation between center-of-mass velocity and linear momentum.

Ambiguities challenge the consistency of third post-Newtonian approximations.

Abstract

The orbital dynamics of the binary point-mass systems is ambiguous at the third post-Newtonian order of approximation. The static ambiguity is known to be related to the difference between the Brill-Lindquist solution and the Misner-Lindquist solution of the time-symmetric conformally flat initial value problem for binary black holes. The kinetic ambiguity is noticed to violate in general the standard relation between the center-of-mass velocity and the total linear momentum as demanded by global Lorentz invariance.