{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"8d6b2e991c61a7120153d0a912afb2bd1a316117d570477fb08709e3b0c8e367","created":"2026-10-03T07:18:04Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"63dcbd4afd6445e3ac108db041e24e3fae41b0457886719a580225b6e3c55843","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"grav.kerr-stability.kerr-uniqueness-smooth","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"The no-hair theorem says a settled black hole is fully described by its mass and spin. The classic proofs assume the spacetime is analytic, a far stronger smoothness condition than physics justifies, and without it the result is proved only near Kerr.","posed_since":"","precise":"Prove that every smooth ($C^{\\infty}$, not assumed real-analytic), asymptotically flat, stationary vacuum $3+1$ black hole exterior with a connected non-degenerate horizon is isometric to a Kerr exterior with $\\mid a \\mid < M$. Known results: true under analyticity (Hawking, Carter, Robinson), under conditions on the bifurcate sphere (Ionescu and Klainerman 2009), and for small perturbations of Kerr (Alexakis, Ionescu, Klainerman 2010). An answer is a proof or a smooth non-Kerr counterexample.","problem_ref":null,"references":"","settled_by":"A rigidity theorem for smooth stationary vacuum black holes without analyticity or closeness-to-Kerr assumptions.","status_note":"Proved near Kerr (2010); the general smooth case is open as of 2026 (moderate confidence).","title":"Is Kerr the only smooth stationary vacuum black hole?","topic_ref":"be2aa7f5f2ad85604c5d4874af362613267361a54ca383af83a420f7d1ef76b3"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"d974f419a460fc96463e335bab43c54411e0d85616a7008e717faac39871562e","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"da688acf4fab3bf6a4339747153b7df02423bbc3c7bef8836ba67571fea66bfc","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"NXqQsTP1LWOOocKBU77K5mPWnmpaS5wiWyNeXziBvu4fXgOYeoIu1cDZYEqxQxuPKva8PLVjnwFZ0seHcvg6DA"},"schema":"pubphys.envelope/1"},"record_hash":"d974f419a460fc96463e335bab43c54411e0d85616a7008e717faac39871562e","leaf_index":1486}