Prove generic Lipschitz (or C1) inextendibility of near-Kerr MGHDs.

Summary

Prove generic Lipschitz (or C1) inextendibility of near-Kerr MGHDs.

Why this matters

Targets the revised SCC expected after C0-extendibility.

Exact scope

Background / setting

asymptotically flat general relativity context; see family and coupling tags for matter model.

Equation type

PDE level: full-einstein.

Linearity

linearized

Regularity

Smooth / Sobolev hypotheses must be stated precisely in any final theorem; this provisional entry does not fix minimal regularity.

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

Theorem status follows literature as summarized in known results and references (not upgraded without verified solution pointers).

Problem statement

Prove generic Lipschitz (or C1) inextendibility of near-Kerr MGHDs.

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: Context: Targets the revised SCC expected after C0-extendibility.

What remains open

Prove generic Lipschitz (or C1) inextendibility of near-Kerr MGHDs.

Mathematical prerequisites

Match hypotheses to primary sources cited on this page; state minimal regularity, gauge class, and parameter windows in any claimed theorem.

Completion criteria

Prove a theorem or give a rigorous counterexample that matches the scoped statement under explicitly listed hypotheses.

Implications if solved

Impact depends on the solved formulation; sharpen once the statement is pinned to a literature-compatible theorem.

Formal verification suitability

FV: low

Global PDE or phenomenological target; lemma-level formalization may be possible after scoping.

See Formal verification for how this database uses these labels.

References

• primary The interior of dynamical vacuum black holes I: $C^0$-stability of the Kerr Cauchy horizon — Dafermos, Luk (2017)
  Foundational interior/Cauchy-horizon stability in $Lambda=0$ vacuum; context for SCC-type questions.
• primary Stability of Minkowski space and polyhomogeneity of the metric — Hintz, Vasy (2017)
  Sharp null-infinity asymptotics in a nonlinear vacuum setting; template for peeling/polyhomogeneous questions.

Related problems

Related by shared tags

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

• K-101 — Strong Cosmic Censorship threshold for Kerr interiors
• K-104 — Generic $C^2$- or Lipschitz-inextendibility of near-Kerr MGHDs
• K-111 — Global interior boundary type: null versus spacelike pieces
• K-610 — Establish sharp SCC thresholds in Kerr interiors for C0 vs C1 vs C2 formulations.
• 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

Source manifest: N-011 (expansion_from_manifest.tsv). Numeric footnotes from the original table are not reproduced in this repository.