The need for a nonlocal expansion in general relativity

TL;DR

This paper suggests that the traditional post-Newtonian approximation in general relativity may fail for extended rotating bodies with significant angular momentum, indicating a need for a new nonlocal effective field theory.

Contribution

It introduces a new dimensionless quantity to detect the breakdown of the approximation and evaluates it using analytical solutions and observational data.

Findings

The approximation may fail for wide-extended rotating bodies with significant angular momentum.

A new effective field theory might be necessary to account for nonlocal angular momentum effects.

Estimates suggest potential implications for galaxies, binary systems, and cosmic structures.

Abstract

Motivated by known facts about effective field theory and non-Abelian gauge theory, we argue that the post-Newtonian approximation might fail even in the limit of weak fields and small velocities for wide-extended rotating bodies, where angular momentum spans significant spacetime curvature. We construct a novel dimensionless quantity that samples this breakdown, and we evaluate it by means of existing analytical solutions of rotating extended bodies and observational data. We give estimates for galaxies and binary systems, as well as our home in the Cosmos, Laniakea. We thus propose that a novel effective field theory of general relativity might be needed to account for the onset of nonlocal angular momentum effects.