{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"cfed5bb64915142ceffc83e39d7d7e5c4f90369ee019460efb1acc08ceddfd46","created":"2026-10-03T07:18:04Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"4bb435ee4b2d1aa8a159315225d230a5e2a9881bd631484b379ac27dfea5c910","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"mechanism","assisted_by":[],"external_id":"grav.kerr-stability.extremal-kerr-fate","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"At maximum spin, small disturbances do not die away at the horizon: some of their derivatives grow forever, an effect found in 2011 by the mathematician Stefanos Aretakis. Whether this growth destroys the extremal black hole in the full theory is unknown.","posed_since":"2011","precise":"Linear fields on extremal Kerr ($a=M$) show the Aretakis instability (non-decay and growth of transversal derivatives along the horizon) and azimuthal instabilities (Gajic 2023). Determine the nonlinear evolution of vacuum data near extremal Kerr: whether solutions settle to a subextremal or extremal Kerr exterior, whether horizon instabilities produce singular behavior, and the codimension of the set of data that remain extremal. An answer is a theorem describing the asymptotic state.","problem_ref":null,"references":"","settled_by":"A nonlinear theorem for vacuum perturbations of extremal Kerr describing the late-time state and horizon regularity.","status_note":"Nonlinear stability with the Aretakis horizon instability is proved for extremal Reissner-Nordstrom in spherical symmetry (Angelopoulos, Kehle, Unger, arXiv:2410.16234, 2024); vacuum extremal Kerr is open as of 2026.","title":"Nonlinear fate of perturbed extremal Kerr black 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