Recognizing that non-perturbative GR effects can be important in circumstances conventionally considered to be non-relativistic, is a big step forward.
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.
Marco Galoppo, Giorgio Torrieri, "When Weak Fields Arent Weak: Post-Newtonian effective theory and the Dark Matter Puzzle" arXiv:2605.13557 (May 13, 2026) (Honorable mention, Gravity Research Foundation essay competition 2026).
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