Prove stability/instability of the Cauchy horizon for Kerr-de Sitter under linearized gravity with sharp norms.
Summary
Prove stability/instability of the Cauchy horizon for Kerr-de Sitter under linearized gravity with sharp norms.
Why this matters
Extends SCC analysis to rotating Lambda>0 setting.
Exact scope
- Background / setting
- de sitter general relativity context; see family and coupling tags for matter model.
- Equation type
- PDE level: linearized-gravity.
- 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
- de sitter
- 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 stability/instability of the Cauchy horizon for Kerr-de Sitter under linearized gravity with sharp norms.
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: Extends SCC analysis to rotating Lambda>0 setting.
What remains open
Prove stability/instability of the Cauchy horizon for Kerr-de Sitter under linearized gravity with sharp norms.
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-108 — Strong cosmic censorship in rotating $\Lambda>0$ black-hole interiors (conditional on a spectral–interior bridge)
- K-608 — Prove unconditional nonlinear stability of slowly rotating Kerr-de Sitter.
- K-609 — Prove conditional nonlinear stability of Kerr-de Sitter in the full subextremal range under explicit mode-stability assumptions.
- K-665 — Prove quantitative mode stability for Kerr-de Sitter in full subextremal range and feed into nonlinear stability.
- K-112 — Teukolsky interior asymptotics beyond the current state of the art
- K-613 — Build an explicit linearized-gravity scattering map exterior to Cauchy horizon for Kerr.
- K-614 — Prove sharp asymptotics for the Teukolsky field in the Kerr interior (Price law inside).
- K-641 — Prove the interior blue-shift blow-up for linearized gravity without auxiliary decay assumptions (purely from generic initial data).
Editorial / maintainer notes
Source manifest: N-067 (expansion_from_manifest.tsv). Numeric footnotes from the original table are not reproduced in this repository.