{"paper":{"title":"A master equation for Carter-separable stationary axisymmetric spacetimes and compatible sources","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Hyeong-Chan Kim","submitted_at":"2026-06-02T15:12:36Z","abstract_excerpt":"We show that the remaining diagonal Einstein equations in the Carter-projective sector of stationary axisymmetric spacetimes are equivalent to a single sourced master equation. The projective structure is taken as the input fixed by the off-diagonal Einstein equations. In the anti-aligned exponential branch, which contains the Kerr--Carter and Pleba\\'nski--Demia\\'nski real section, the remaining diagonal Einstein system reduces to \\[\n  \\mathcal L_{\\rm CP}[\\Delta,Y]\n  =16\\pi\\Sigma \\left( T_{\\hat0\\hat0}+T_{\\hat3\\hat3} \\right), \\] where \\(\\Delta(r)\\) and \\(Y(x)\\) are the radial and angular struct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03758","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.03758/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}