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K-104

Generic $C^2$- or Lipschitz-inextendibility of near-Kerr MGHDs

Open Classical frontier Open in literature Mostly scoped Interior / SCC Pure math FV: medium
Near-Kerr (vacuum) Asymptotically flat Vacuum Full Einstein InteriorNonlinear

Summary

Generic $C^2$- or Lipschitz-inextendibility of near-Kerr MGHDs

Why this matters

This is the strongest currently plausible version of SCC for Kerr-type interiors.

Exact scope

Background / setting
Asymptotically flat four-dimensional general relativity unless the statement specifies otherwise. Cauchy horizon / interior regularity formulations of strong cosmic censorship are in play; distinguish $C^0$ vs higher regularity notions.
Equation type
PDE level: full-einstein.
Linearity
Includes or emphasizes nonlinear dynamics.
Regularity
State intended regularity class for extensions across horizons explicitly (e.g. $C^0$, Lipschitz, $C^2$).
Parameter regime
Subextremal Kerr interior up to Cauchy horizons; specify SCC regularity class ($C^0$, Lipschitz, $C^k$) in the theorem.
Asymptotics
asymptotically-flat
Gauge / formulation
State gauge/fixing class compatible with cited stability or interior programs (e.g. generalized harmonic, double-null interior charts).

Status explanation

Entry imported without two independent bibliographic pointers in this repository; treat theorem-level claims as unverified here.

Problem statement

Show that although $C^0$ extensions can exist, generic near-Kerr vacuum developments admit no extension with enough regularity to preserve a meaningful Einstein evolution across the Cauchy horizon.

What is already known

  • $C^0$-extendibility and weak regularity across Cauchy horizons are understood in substantial $Lambda=0$ vacuum settings (Dafermos–Luk program); higher regularity and $Lambda>0$ charged models require separate hypotheses.
    Regime: Dynamical vacuum near Kerr, $Lambda=0$ baseline; contrast with $Lambda>0$ scalar scans.
    Sets what “partial” interior control means before claiming generic blow-up or extendibility.
  • Linear scalar and Teukolsky-type decay on fixed subextremal Kerr exteriors is highly developed and feeds conditional interior instability heuristics.
    Regime: Linearized fields on exact Kerr/Kerr–Newman.
    Supplies quantitative decay exponents used in bridge hypotheses to inner horizons.
  • Polyhomogeneous/null-infinity technology exists for nonlinear Minkowski and some linearized Kerr contexts; sharp nonlinear near-Kerr peeling is not packaged as one theorem.
    Regime: Null infinity / linearized models.
    Separates radiation asymptotics from interior SCC targets.

Progress summary: Partial progress exists in adjacent regimes;

What remains open

A complete answer must specify the regularity class, prove generic blow-up of the corresponding geometric quantity, and rule out every extension in that class.

Mathematical prerequisites

Curvature lower bounds; regularity comparison; extension theory; blow-up of connection or curvature invariants.

Completion criteria

A complete answer must specify the regularity class, prove generic blow-up of the corresponding geometric quantity, and rule out every extension in that class.

Implications if solved

Would restore deterministic predictability at the correct mathematical regularity level.

Formal verification suitability

FV: medium

Some subquestions may formalize before the full statement.

See Formal verification for how this database uses these labels.

References

Related problems

K-101
Strong Cosmic Censorship threshold for Kerr interiors
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K-102
Derive the interior theorem directly from exterior data
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Vacuum curvature blow-up rates on the Kerr Cauchy horizon
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K-105
Critical horizon-decay exponent controlling extendibility
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K-106
Genericity of lower bounds for linearized-gravity interior instability
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K-107
Scattering map to the Cauchy horizon for linearized gravity
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K-108
Strong cosmic censorship in rotating $\Lambda>0$ black-hole interiors (conditional on a spectral–interior bridge)
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Near-extremal interior scaling laws
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K-110
Global bifurcation-sphere completion for perturbed Kerr-type interiors (vacuum, $\Lambda=0$, Dafermos–Luk class)
Partial progress
K-111
Global interior boundary type: null versus spacelike pieces
Open
K-112
Teukolsky interior asymptotics beyond the current state of the art
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Related by shared tags

Heuristic matches on family, cluster, equation level, asymptotics, and relevance.

  • K-610 — Establish sharp SCC thresholds in Kerr interiors for C0 vs C1 vs C2 formulations.
  • K-611 — Prove generic Lipschitz (or C1) inextendibility of near-Kerr MGHDs.
  • K-615 — Show that small vacuum perturbations of Kerr produce weak null singularities generically at the Cauchy horizon.
  • K-631 — Prove a unified framework for gauge choices in nonlinear black-hole stability compatible with $\mathcal{I}^+$ expansions and interior analysis.
  • K-643 — Establish a sharp criterion for when Kerr interior admits C0 extension vs stronger regularity failure (in terms of horizon tails).
  • K-644 — Prove a full nonlinear characteristic IVP theorem from event-horizon data to the interior boundary in near-Kerr vacuum.

Editorial / maintainer notes

Open: no complete theorem matching the statement is currently recorded on this site. : tighten if community consensus differs.

Last updated: 2026-04-05 · Last verified (editorial): 2026-04-06 (bulk-editorial-fixes) · Edit on GitHub →