Clusters Interior / SCC

Interior / SCC

Cauchy horizon structure, blue-shift instability, strong cosmic censorship, and the singularity structure of the Kerr interior.

27 problems 23 open 3 partial 0 needs review
By family (this cluster)
  • Near-Kerr (vacuum) (16)
  • Exact Kerr (7)
  • Kerr–de Sitter (2)
  • NHEK / near-horizon (1)
  • Kerr–Newman (1)
By relevance
  • Pure math (25)
  • Mixed (2)
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-101
Strong Cosmic Censorship threshold for Kerr interiors
Open Near-Kerr (vacuum) Pure math
K-102
Derive the interior theorem directly from exterior data
Open Exact Kerr Pure math
K-103
Vacuum curvature blow-up rates on the Kerr Cauchy horizon
Open Exact Kerr Pure math
K-104
Generic $C^2$- or Lipschitz-inextendibility of near-Kerr MGHDs
Open Near-Kerr (vacuum) Pure math
K-105
Critical horizon-decay exponent controlling extendibility
Open Exact Kerr Pure math
K-106
Genericity of lower bounds for linearized-gravity interior instability
Open Exact Kerr Pure math
K-107
Scattering map to the Cauchy horizon for linearized gravity
Open Exact Kerr Mixed
K-108
Strong cosmic censorship in rotating $\Lambda>0$ black-hole interiors (conditional on a spectral–interior bridge)
Conditional Kerr–de Sitter Mixed
K-109
Near-extremal interior scaling laws
Open NHEK / near-horizon Pure math
K-110
Global bifurcation-sphere completion for perturbed Kerr-type interiors (vacuum, $\Lambda=0$, Dafermos–Luk class)
Partial progress Exact Kerr Pure math
K-111
Global interior boundary type: null versus spacelike pieces
Open Near-Kerr (vacuum) Pure math
K-112
Teukolsky interior asymptotics beyond the current state of the art
Open Exact Kerr Pure math
K-610
Establish sharp SCC thresholds in Kerr interiors for C0 vs C1 vs C2 formulations.
Open Near-Kerr (vacuum) Pure math
K-611
Prove generic Lipschitz (or C1) inextendibility of near-Kerr MGHDs.
Open Near-Kerr (vacuum) Pure math
K-613
Build an explicit linearized-gravity scattering map exterior to Cauchy horizon for Kerr.
Open Near-Kerr (vacuum) Pure math
K-614
Prove sharp asymptotics for the Teukolsky field in the Kerr interior (Price law inside).
Open Near-Kerr (vacuum) Pure math
K-615
Show that small vacuum perturbations of Kerr produce weak null singularities generically at the Cauchy horizon.
Partial progress Near-Kerr (vacuum) Pure math
K-631
Prove a unified framework for gauge choices in nonlinear black-hole stability compatible with $\mathcal{I}^+$ expansions and interior analysis.
Open Near-Kerr (vacuum) Pure math
K-641
Prove the interior blue-shift blow-up for linearized gravity without auxiliary decay assumptions (purely from generic initial data).
Open Near-Kerr (vacuum) Pure math
K-643
Establish a sharp criterion for when Kerr interior admits C0 extension vs stronger regularity failure (in terms of horizon tails).
Open Near-Kerr (vacuum) Pure math
K-644
Prove a full nonlinear characteristic IVP theorem from event-horizon data to the interior boundary in near-Kerr vacuum.
Open Near-Kerr (vacuum) Pure math
K-645
Quantify the nonlinear backreaction of Price-law tails on Kerr interior geometry (mass inflation vs weak null singularity).
Open Near-Kerr (vacuum) Pure math
K-654
Prove robust boundedness/decay for scalar waves at the Kerr Cauchy horizon in full range and sharp regularity.
Partial progress Near-Kerr (vacuum) Pure math
K-666
Prove SCC threshold for Kerr-de Sitter and Kerr-Newman-de Sitter with explicit dependence on spectral gap.
Open Kerr–Newman Pure math
K-667
Prove stability/instability of the Cauchy horizon for Kerr-de Sitter under linearized gravity with sharp norms.
Open Kerr–de Sitter Pure math
K-668
Prove a nonlinear interior from exterior theorem: decay on event horizon implies interior weak null singularity.
Open Near-Kerr (vacuum) Pure math
K-698
Prove stability/instability of the Kerr Cauchy horizon for nonlinear vacuum perturbations with genericity (beyond C0).
Open Near-Kerr (vacuum) Pure math