{"paper":{"title":"When Weak Fields Arent Weak: Post-Newtonian effective theory and the Dark Matter Puzzle","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Post-Newtonian expansions become unreliable in weak fields when global conserved charges are absent and dynamics are non-integrable.","cross_cats":["hep-ph"],"primary_cat":"gr-qc","authors_text":"Giorgio Torrieri, Marco Galoppo","submitted_at":"2026-05-13T14:00:12Z","abstract_excerpt":"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 t"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the validity of post-Newtonian truncations depends primarily on local potentials and velocities being small, without needing to account for global properties such as the presence of conserved charges and integrability of the dynamics.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Post-Newtonian effective theory breaks down in generic many-body relativistic dynamics despite small local potentials and velocities, due to sensitivity from absent conserved charges and non-integrability, supplying a criterion for reliable weak-field mass inference relevant to the dark matter","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Post-Newtonian expansions become unreliable in weak fields when global conserved charges are absent and dynamics are non-integrable.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"56fa6e8811b262d0f723108a00e297e00f61f59adcd8b3100b11c0131dabb733"},"source":{"id":"2605.13557","kind":"arxiv","version":1},"verdict":{"id":"a8f51728-673a-44c1-bfe2-3651c259a8e0","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:14:49.870789Z","strongest_claim":"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.","one_line_summary":"Post-Newtonian effective theory breaks down in generic many-body relativistic dynamics despite small local potentials and velocities, due to sensitivity from absent conserved charges and non-integrability, supplying a criterion for reliable weak-field mass inference relevant to the dark matter","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the validity of post-Newtonian truncations depends primarily on local potentials and velocities being small, without needing to account for global properties such as the presence of conserved charges and integrability of the dynamics.","pith_extraction_headline":"Post-Newtonian expansions become unreliable in weak fields when global conserved charges are absent and dynamics are non-integrable."},"references":{"count":33,"sample":[{"doi":"","year":null,"title":"for further technical details). What is tantalizing is that the diagnostic parameter introduced here is small precisely in regimes where the post-Newtonian expansion is quantitatively well tested: ˜αi","work_id":"2818e20c-0989-4a4f-9981-88c326c427cb","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1973,"title":"C. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation(W. H. Freeman, San Francisco, 1973)","work_id":"6c99d480-9e49-483e-bb1b-98c4dbbc0b46","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2005,"title":"G. Bertone, D. Hooper, and J. Silk, Particle dark matter: Evidence, candidates and constraints, Phys. Rept.405, 279 (2005)","work_id":"bc1f30ab-f5db-4e0b-8bf4-d6c38a0f1364","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2012,"title":"B. Famaey and S. McGaugh, Modified Newtonian Dynamics (MOND): Observational Phe- nomenology and Relativistic Extensions, Liv. Rev. Rel.15, 10 (2012)","work_id":"b282b4b1-904c-477f-b689-f88a654e8f6e","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2014,"title":"E. Poisson and C. M. Will,Gravity, Newtonian, Post-Newtonian, Relativistic(Cambridge 10 University Press, 2014)","work_id":"6d272525-1503-45ad-ac95-2b0231f4cf27","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":33,"snapshot_sha256":"934f670685cf0c846b91dc64513711d729307f47a6f88b9764498223fa88c19b","internal_anchors":1},"formal_canon":{"evidence_count":1,"snapshot_sha256":"973ee112afd56997829c2e1e09aa72b50768e71353fc127cd51b29a78072e5d5"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}