The need for a nonlocal expansion in general relativity

TL;DR

The paper argues that the standard post-Newtonian expansion of general relativity can break down for extended rotating bodies when curvature varies across the structure, even in weak-field regimes. It introduces a nonlocal, dimensionless expansion parameter $\tilde{\alpha}$ defined via a bi-tensor coupling between the Riemann tensor and special-relativistic angular momentum densities, with leading expressions that quantify deviations from PN behavior. By evaluating $\tilde{\alpha}$ for systems ranging from stellar binaries to the Laniakea supercluster, the authors find $\tilde{\alpha} \ll 1$ for compact, binary-like systems but $\tilde{\alpha} \gg 1$ for wide, high-angular-momentum structures like disc galaxies and Laniakea, suggesting a breakdown of the PN expansion and motivating a nonlocal EFT of GR. They discuss potential implications for dark matter inferences and outline observational and numerical tests, including upcoming surveys (e.g., Euclid, DESI, LSST) and the development of a Wilson-line–type EFT framework to capture nonlocal angular-momentum effects in gravity.

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.