Post-Newtonian gravity may quietly fail in many-body systems

Post-Newtonian theory is routinely trusted whenever gravitational fields are weak and motions are slow — two conditions satisfied across most astrophysical systems. This paper argues that in generic many-body settings, the lack of globally conserved charges and non-integrable dynamics can amplify angular-momentum exchanges across curved, inhomogeneous backgrounds, causing the perturbative expansion to fail even when the local expansion parameters look small. The authors derive an explicit criterion for when this breakdown occurs, offering a systematic check on whether a given system can be trusted to yield reliable mass inferences — directly relevant to the dark matter problem, where such inferences are foundational.