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”.

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
Open Near-Kerr (vacuum) Pure math
K-202
Full linear theory for extremal Kerr (spin 2)
Open Near-Kerr (vacuum) Pure math
K-203
Nonlinear fate of Aretakis instability
Open Near-Kerr (vacuum) Pure math
K-204
Uniform estimates in the surface-gravity limit $\kappa \to 0$
Open Related rotating BH Pure math
K-205
Rigorous near-horizon scattering theory for NHEK
Open NHEK / near-horizon Mixed
K-206
Extremal interior SCC and Cauchy-horizon regularity
Open NHEK / near-horizon Pure math
K-207
Extremal tail asymptotics versus conserved charges
Open Related rotating BH Pure math
K-208
Near-extremal QNM accumulation and branch-cut structure
Open Related rotating BH Physics-facing
K-209
Codimension and modulation theory for extremal endstates
Open Related rotating BH Pure math
K-509
Charge–tail correspondence in the extremal limit
Needs review Kerr–Newman Mixed
K-657
Prove nonlinear evolution of near-horizon conserved quantities in extremal Kerr produces curvature singularity (or not).
Open Near-Kerr (vacuum) Pure math
K-658
Prove linear stability/instability classification for extremal Kerr-Newman under coupled perturbations.
Open Kerr–Newman Pure math