Static two-body potential at fifth post-Newtonian order

TL;DR

This paper calculates the static gravitational potential between two compact bodies up to fifth post-Newtonian order using effective field theory, providing new high-order contributions and rederiving lower-order results.

Contribution

It introduces a novel method to derive static post-Newtonian contributions at higher orders from lower order results within effective field theory.

Findings

Recomputed 1PN and 3PN static potentials.

Derived the first static 5PN contribution.

Showed a factorization property simplifying calculations.

Abstract

We determine the gravitational interaction between two compact bodies up to the sixth power in Newton's constant GN, in the static limit. This result is achieved within the effective field theory approach to General Relativity, and exploits a manifest factorization property of static diagrams which allows to derive static post Newtonian (PN) contributions of (2n+1)-order in terms of lower order ones. We recompute in this fashion the 1PN and 3PN static potential, and present the novel 5PN contribution.