{"paper":{"title":"Quasi-topological gravity for 4-dimensional Taub-NUT, near-horizon extreme Kerr, and swirling symmetries","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Aimeric Coll\\'eaux, Ivan Kol\\'a\\v{r}, Tom\\'a\\v{s} M\\'alek","submitted_at":"2026-06-16T11:00:37Z","abstract_excerpt":"We classify 4-dimensional gravitational theories with integrability properties analogous to quasi-topological gravity, but for metrics with the symmetries of spherical, hyperbolic, and planar Schwarzschild and Taub-NUT solutions, their double-Wick-rotated counterparts - the B-metrics, the near-horizon extreme Kerr, and the swirling universe - and the Eguchi-Hanson instanton. These are the symmetries that allow consistent reductions (principle of symmetric criticality) with 4 Killing vectors and 3-dimensional orbits. Considering theories depending only on the Riemann tensor, we show that, for t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17784","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/2606.17784/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"}