Clusters → Rigidity / Uniqueness
Rigidity / Uniqueness
Stationary black hole characterization, hidden symmetries, Mars–Simon tensor, and near-Kerr recognition theorems.
27 problems 23 open 2 partial 2 needs review
By family (this cluster)
- Near-Kerr (vacuum) (17)
- Exact Kerr (8)
- Kerr–Newman (2)
By relevance
- Pure math (27)
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
Algebraic uniqueness of quadratic symmetry operators commuting with $\Box_g$ on exact Kerr ($\mathcal{D}_{\le 2}$ class)
K-508
Stability or obstruction for approximate Killing–Yano tensors near Kerr
K-510
Ernst equation on stationary axisymmetric vacuum exteriors — sharp uniqueness class for asymptotically flat Kerr (boundary-value formulation)
K-617
Prove a quantitative distance-to-Kerr estimate from a small invariant (Mars-Simon-type) with computable constants.
K-618
Prove global Kerr uniqueness without analyticity under minimal smoothness/decay hypotheses.
K-619
Prove uniqueness of stationary black holes with small deviations in asymptotic charges (effective inverse problems).
K-626
Prove a Kerr inverse problem: determine (M,a) from finitely many resonances with stability estimates.
K-633
Prove that near-Kerr spacetimes admit approximate Carter operators with controlled commutators (usable in PDE estimates).
K-634
Classify all second-order symmetry operators commuting with the scalar wave operator on Kerr.
K-646
Prove global uniqueness/rigidity for Kerr with minimal assumptions on horizon regularity and connectedness.
K-647
Prove a minimal-data theorem: finite set of horizon multipoles determines Kerr parameters with stability bounds.
K-648
Prove existence/uniqueness of approximate Kerr solutions given approximate Killing spinors (computable error-to-parameter map).
K-675
Prove uniqueness/stability of event-horizon generators and their expansion/shear in near-Kerr evolution.
K-686
Prove an effective theorem translating small Mars-Simon tensor into existence of approximate Killing spinors.
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.