Poincar\'e invariance in the ADM Hamiltonian approach to the general relativistic two-body problem

TL;DR

This paper demonstrates that the momentum-dependent ambiguity in the 3rd post-Newtonian two-body Hamiltonian can be uniquely fixed by enforcing Poincaré invariance, with explicit construction of the Poincaré generators.

Contribution

It shows that global Poincaré invariance uniquely determines the previously ambiguous regularization parameter in the Hamiltonian.

Findings

The ambiguity in the Hamiltonian is resolved by Poincaré invariance.

Explicit phase-space generators for the Poincaré algebra are constructed.

The approach clarifies the structure of the 3rd post-Newtonian two-body problem.

Abstract

A previously found momentum-dependent regularization ambiguity in the third post-Newtonian two point-mass Arnowitt-Deser-Misner Hamiltonian is shown to be uniquely determined by requiring global Poincar\'e invariance. The phase-space generators realizing the Poincar\'e algebra are explicitly constructed.