{"paper":{"title":"A mathematical comment on gravitational waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math.AC","math.AP","math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"Jean-Fran\\c{c}ois Pommaret (CERMICS)","submitted_at":"2017-08-22T12:09:42Z","abstract_excerpt":"In classical General Relativity, the way to exhibit the equations for the gravitational waves is based on two \"tricks\" allowing to transform the Einstein equations after linearizing them over the Minkowski metric. With specific notations used in the study of {\\it Lie pseudogroups} of transformations of an $n$-dimensional manifold, let $\\Omega=({\\Omega}\\_{ij}={\\Omega}\\_{ji})$ be a perturbation of the non-degenerate metric $\\omega=({\\omega}\\_{ij}={\\omega}\\_{ji})$ with $det(\\omega)\\neq 0$ and call ${\\omega}^{-1}=({\\omega}^{ij}={\\omega}^{ji})$ the inverse matrix appearing in the Dalembertian opera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06575","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}