Show that small vacuum perturbations of Kerr produce weak null singularities generically at the Cauchy horizon.
Summary
Show that small vacuum perturbations of Kerr produce weak null singularities generically at the Cauchy horizon.
Why this matters
Converts extendible but singular heuristics into theorem-level genericity.
Exact scope
- Background / setting
- asymptotically flat general relativity context; see family and coupling tags for matter model.
- Equation type
- PDE level: full-einstein.
- Linearity
- nonlinear
- 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
Partial results exist in adjacent regimes (see references); sharp alignment with this page’s exact target remains open.
Problem statement
Show that small vacuum perturbations of Kerr produce weak null singularities generically at the Cauchy horizon.
What is already known
- Named papers in the reference list establish partial or neighboring results under explicit hypotheses; treat those as the proved baseline.Regime: As stated in cited references (often restricted parameters or linearized settings).Orients readers to literature without equating it with the full title-length target.
Progress summary: Manifest rationale: Converts extendible but singular heuristics into theorem-level genericity.
What remains open
Show that small vacuum perturbations of Kerr produce weak null singularities generically at the Cauchy horizon.
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
- 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-611 — Prove generic Lipschitz (or C1) inextendibility of near-Kerr MGHDs.
- 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-015 (expansion_from_manifest.tsv). Numeric footnotes from the original table are not reproduced in this repository.