Dimensional regularization of the gravitational interaction of point masses in the ADM formalism

TL;DR

This paper applies dimensional regularization within the ADM formalism to derive a finite, unambiguous 3rd post-Newtonian Hamiltonian for two-point-mass systems in general dimensions, resolving previous regularization ambiguities.

Contribution

It introduces a dimensional continuation method to regularize the 3rd post-Newtonian ADM Hamiltonian, providing new details and ensuring a unique result in the limit as dimension approaches three.

Findings

Regularization ambiguities are resolved by dimensional continuation.

A finite, unique 3rd post-Newtonian Hamiltonian is obtained.

Unpublished details of the dimensional-continuation computation are presented.

Abstract

The ADM formalism for two-point-mass systems in $d$ space dimensions is sketched. It is pointed out that the regularization ambiguities of the 3rd post-Newtonian ADM Hamiltonian considered directly in $d=3$ space dimensions can be cured by dimensional continuation (to complex $d$'s), which leads to a finite and unique Hamiltonian as $d\to3$. Some so far unpublished details of the dimensional-continuation computation of the 3rd post-Newtonian two-point-mass ADM Hamiltonian are presented.