Clusters → Extremal / Near-Extremal
Extremal / Near-Extremal
Zero surface gravity, Aretakis instability, NHEK geometry, and the transition from subextremal to extremal dynamics.
18 problems 17 open 1 partial 0 needs review
By family (this cluster)
- Near-Kerr (vacuum) (9)
- Related rotating BH (4)
- NHEK / near-horizon (3)
- Kerr–Newman (2)
By relevance
- Pure math (15)
- Mixed (2)
- Physics-facing (1)
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-201
Nonlinear codimension-1 stability of extremal Kerr with horizon hair
K-202
Full linear theory for extremal Kerr (spin 2)
K-203
Nonlinear fate of Aretakis instability
K-204
Uniform estimates in the surface-gravity limit $\kappa \to 0$
K-205
Rigorous near-horizon scattering theory for NHEK
K-206
Extremal interior SCC and Cauchy-horizon regularity
K-207
Extremal tail asymptotics versus conserved charges
K-208
Near-extremal QNM accumulation and branch-cut structure
K-209
Codimension and modulation theory for extremal endstates
K-509
Charge–tail correspondence in the extremal limit
K-620
Establish a rigorous nonlinear theory for extremal Kerr dynamics incorporating Aretakis charges.
K-621
Prove a definitive linear stability/instability dichotomy for extremal Kerr spin-2 with sharp norms.
K-622
Prove uniform (in kappa) energy/decay estimates for near-extremal Kerr approaching kappa to 0.
K-623
Build a rigorous scattering theory for NHEK matching to global Kerr exterior at near-extremality.
K-656
Prove decay/growth dichotomy for extremal Kerr perturbations with explicit identification of conserved charges.
K-657
Prove nonlinear evolution of near-horizon conserved quantities in extremal Kerr produces curvature singularity (or not).
K-658
Prove linear stability/instability classification for extremal Kerr-Newman under coupled perturbations.
K-691
Prove that event-horizon redshift estimates remain valid for near-extremal Kerr with uniform constants away from kappa=0.