{"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 holes","topic_ref":"be2aa7f5f2ad85604c5d4874af362613267361a54ca383af83a420f7d1ef76b3"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"7dcb84790739e8d6886e6c27c5d565af1c4babbd5afc83e4b2976bf42ac3bed9","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"7aadd0fad8a368cc2287c1be7cdb028918bae90f1e74aab84bf3f148404b5762","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"7v0r-Z8H4EzPdAuoiewBMt621v3x9GDeytlDN_KNhsk4e_FgnZQ65B0FvSwmb6Zgrv84KYy09Tq2pRc28qKwAA"},"schema":"pubphys.envelope/1"},"record_hash":"7dcb84790739e8d6886e6c27c5d565af1c4babbd5afc83e4b2976bf42ac3bed9","leaf_index":1481}