Vacuum curvature blow-up rates on the Kerr Cauchy horizon
Summary
Vacuum curvature blow-up rates on the Kerr Cauchy horizon
Why this matters
SCC is not just about whether blow-up occurs, but about which geometric quantities diverge and how fast.
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
Prove sharp quantitative blow-up rates for curvature or gauge-invariant gravitational quantities along the Kerr Cauchy horizon for generic perturbations.
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 provide matching upper and lower blow-up rates in a regular frame and show generic nonvanishing of leading coefficients.
Mathematical prerequisites
Nonlinear Bianchi analysis; Teukolsky asymptotics; blue-shift energy estimates; tetrad regularity.
Completion criteria
A complete answer must provide matching upper and lower blow-up rates in a regular frame and show generic nonvanishing of leading coefficients.
Implications if solved
Would make the weak-null-singularity picture quantitative instead of merely qualitative.
Formal verification suitability
FV: medium
Some subquestions may formalize before the full statement.
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
Editorial / maintainer notes
Open: no complete theorem matching the statement is currently recorded on this site. : tighten if community consensus differs.