When Weak Fields Arent Weak: Post-Newtonian effective theory and the Dark Matter Puzzle

TL;DR

This paper challenges the reliability of post-Newtonian theory in weak fields, showing it can break down due to relativistic effects, impacting dark matter inference in astrophysics.

Contribution

It derives a breakdown criterion for post-Newtonian expansions, providing a systematic approach to weak-field mass inference relevant to dark matter studies.

Findings

Post-Newtonian theory can fail even in weak fields due to relativistic dynamics.

A criterion is established to identify when post-Newtonian truncations are unreliable.

The results impact methods for dark matter mass inference in astrophysics.

Abstract

Post-Newtonian theory is considered a reliable effective expansion of General Relativity in the weak-field and slow-motion limit. We argue that such a belief is misplaced. In generic many-body relativistic dynamics, the absence of globally conserved charges in the region of interest and non-integrability can drive strong sensitivity to angular-momentum exchange across inhomogeneous curvature, invalidating naive power counting in an effective theory expansion. Building on general lessons from effective field theory, we derive an explicit breakdown criterion that delineates when post-Newtonian truncations become unreliable despite small local potentials and velocities. This supplies a controlled systematic for weak-field mass inference, relevant to the dark matter puzzle in astrophysics and cosmology.