{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"10567d7bd9bde8c615eb80bac4fd09e0c828e6b460da136f96ca5e69f7bd361d","created":"2026-10-03T07:18:04Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"f766ce044ddbaca21abc5130008c6a4ad8abe70a096f91a0ad184fc1b19170e1","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"grav.kerr-stability.kerr-ads","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"In anti-de Sitter space, a model universe with a reflecting boundary, waves cannot escape and may concentrate into ever smaller scales. Even empty anti-de Sitter space is unstable, and the fate of its black holes is unknown.","posed_since":"","precise":"For Kerr-AdS with reflecting boundary conditions at conformal infinity, linear waves decay only logarithmically in time (Holzegel and Smulevici), and superradiant instabilities occur when $\\Omega_{H}\\ell > 1$, with $\\Omega_{H}$ the horizon angular velocity and l the AdS radius. Determine whether small perturbations of Kerr-AdS with $\\Omega_{H}\\ell < 1$ remain small for all time or develop turbulent cascades, and identify the end state when $\\Omega_{H}\\ell > 1$. An answer is a theorem or convergent numerical evidence.","problem_ref":null,"references":"","settled_by":"A nonlinear stability or instability theorem for Kerr-AdS, or long-time convergent simulations resolving the cascade.","status_note":"Pure AdS is nonlinearly unstable (Bizon and Rostworowski 2011 numerics; proved for Einstein-null dust by Moschidis 2017-2018); Kerr-AdS is open as of 2026.","title":"Are Kerr-AdS black holes nonlinearly stable with reflecting boundary conditions?","topic_ref":"be2aa7f5f2ad85604c5d4874af362613267361a54ca383af83a420f7d1ef76b3"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"833438e66c6b43870755bc72ad04ee16af545a1fd9dcd58d349a93c1911b8a92","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"f9c0ad3ac5a09e41d177fc73d40fc11db21355186bea043de1ee1b1585f0c59d","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"oYdJt21FPYZ4_2UfZqkIhOhMuG7rz1qOsmPhYaAw9hA2dxhqZNUMvg9hcbd97ZsAofUQtsMnSZkShtCuvGn4AQ"},"schema":"pubphys.envelope/1"},"record_hash":"833438e66c6b43870755bc72ad04ee16af545a1fd9dcd58d349a93c1911b8a92","leaf_index":1483}