{"paper":{"title":"General orbital perturbation theory in Schwarzschild space-time","license":"http://creativecommons.org/licenses/by/4.0/","headline":"General relativistic Gaussian equations govern the evolution of osculating orbital elements in Schwarzschild spacetime under arbitrary perturbing forces.","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Claus L\\\"ammerzahl, Eva Hackmann, Oleksii Yanchyshen","submitted_at":"2026-01-23T16:53:00Z","abstract_excerpt":"We derive general relativistic Gaussian equations for osculating elements for orbits under the influence of a perturbing force without any restrictions in an underlying Schwarzschild space-time. Such a formulation provides a way to describe the evolution of orbital parameters in strong gravity relativistic settings. As examples of external forces we considered Kerr and $q$-metric space-times generated forces, for which we solve equations for osculating elements in linear approximation. For the Kerr space-time in the post-Newtonian limit, our result reproduces the well-known Lense--Thirring pre"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We derive general relativistic Gaussian equations for osculating elements for orbits under the influence of a perturbing force without any restrictions in an underlying Schwarzschild space-time.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That osculating orbital elements remain well-defined and their evolution follows Gaussian-type equations in full general relativity for arbitrary perturbing forces, with linear approximation sufficient for the Kerr and q-metric examples.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Derives unrestricted general relativistic Gaussian perturbation equations for osculating orbital elements in Schwarzschild spacetime, with linear solutions for Kerr and q-metric perturbations that recover Lense-Thirring precession.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"General relativistic Gaussian equations govern the evolution of osculating orbital elements in Schwarzschild spacetime under arbitrary perturbing forces.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"06c39ea3ee899f7953431e5ff808454f9c8dadffd1ab9d79b120370496b2b8b9"},"source":{"id":"2601.16887","kind":"arxiv","version":2},"verdict":{"id":"4f6d21f8-7d9c-4cec-a8d8-4bfa89e505e6","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T11:32:50.848905Z","strongest_claim":"We derive general relativistic Gaussian equations for osculating elements for orbits under the influence of a perturbing force without any restrictions in an underlying Schwarzschild space-time.","one_line_summary":"Derives unrestricted general relativistic Gaussian perturbation equations for osculating orbital elements in Schwarzschild spacetime, with linear solutions for Kerr and q-metric perturbations that recover Lense-Thirring precession.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That osculating orbital elements remain well-defined and their evolution follows Gaussian-type equations in full general relativity for arbitrary perturbing forces, with linear approximation sufficient for the Kerr and q-metric examples.","pith_extraction_headline":"General relativistic Gaussian equations govern the evolution of osculating orbital elements in Schwarzschild spacetime under arbitrary perturbing forces."},"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"}