Clusters → Extremal / Near-Extremal
Extremal / Near-Extremal
Zero surface gravity, Aretakis instability, NHEK geometry, and the transition from subextremal to extremal dynamics.
12 problems 11 open 0 partial 1 needs review
By family (this cluster)
- Near-Kerr (vacuum) (4)
- Related rotating BH (4)
- NHEK / near-horizon (2)
- Kerr–Newman (2)
By relevance
- Pure math (9)
- 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”.
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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-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.