Teukolsky interior asymptotics beyond the current state of the art
Summary
Teukolsky interior asymptotics beyond the current state of the art
Why this matters
Teukolsky asymptotics are currently one of the cleanest windows into gravitational interior instability.
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: scalar-wave, linearized-gravity.
- 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
Extend precise interior asymptotics to both spin signs, prove genericity of leading coefficients, and reconstruct metric perturbations in a regular gauge suited for SCC.
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 cover both radiative scalars, reconstruction, and blow-up consequences in metric-level norms.
Mathematical prerequisites
Teukolsky equations; mode asymptotics; gauge reconstruction; regular frame analysis at the Cauchy horizon.
Completion criteria
A complete answer must cover both radiative scalars, reconstruction, and blow-up consequences in metric-level norms.
Implications if solved
Would make the link between spin-field asymptotics and geometric inextendibility much tighter.
Formal verification suitability
FV: low
Global nonlinear PDE or open-ended dynamics; not a practical first formalization target without major 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
Editorial / maintainer notes
Partial: substantial adjacent results or special cases exist, but the statement as written is not fully settled. : replace with a precise description of what is proved vs. conjectured.