Clusters → Rigidity / Uniqueness
Rigidity / Uniqueness
Stationary black hole characterization, hidden symmetries, Mars–Simon tensor, and near-Kerr recognition theorems.
17 problems 15 open 2 partial 0 needs review
By family (this cluster)
- Near-Kerr (vacuum) (8)
- Exact Kerr (7)
- Kerr–Newman (2)
By relevance
- Pure math (17)
Taxonomy caveat. Cluster placement is a coarse editorial choice. Check each problem’s
family and asymptotics tags — e.g. Kerr–AdS and Kerr–de Sitter entries differ sharply from asymptotically
flat Kerr, even when they sit in “Exterior Stability” or “Interior / SCC”.
Filter the full database on the Problems page (family, asymptotics, FV suitability, …).
Problems in this cluster
K-301
Global smooth Kerr uniqueness without analyticity
K-302
Rigidity for extremal horizons
K-303
Quantitative Kerr characterization via the Mars–Simon tensor
K-304
Near-Kerr rigidity with computable geometric constants
K-305
Kerr characterization from horizon intrinsic data
K-306
Hidden symmetries and approximate Carter-type operators under metric perturbation
K-307
Persistence of normally hyperbolic trapping for dynamical near-Kerr spacetimes
K-308
Rigidity and uniqueness with matter: full Kerr–Newman regime
K-501
Quantitative Mars–Simon tensor gap for near-Kerr stationary vacuum data
K-502
Horizon-data rigidity and effective reconstruction of Kerr parameters
K-503
Uniqueness questions for Carter-type symmetry operators on Kerr
K-508
Stability or obstruction for approximate Killing–Yano tensors near Kerr
K-619
Prove uniqueness of stationary black holes with small deviations in asymptotic charges (effective inverse problems).
K-675
Prove uniqueness/stability of event-horizon generators and their expansion/shear in near-Kerr evolution.
K-687
Prove a black-hole uniqueness theorem for near Kerr-Newman-de Sitter without analyticity in smooth category.
K-696
Formalize: perturbative uniqueness near Kerr using Mars-Simon tensor estimates (machine-checkable Carleman skeleton).
K-697
Prove that Kerr is uniquely determined among stationary vacua by a finite set of multipole moments with stability.