Prove robust boundedness/decay for scalar waves at the Kerr Cauchy horizon in full range and sharp regularity.

Summary

Prove robust boundedness/decay for scalar waves at the Kerr Cauchy horizon in full range and sharp regularity.

Why this matters

Extends interior scalar wave theory beyond known regimes.

Exact scope

Background / setting

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

Equation type

PDE level: scalar-wave.

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

Partial results exist in adjacent regimes (see references); sharp alignment with this page’s exact target remains open.

Problem statement

Prove robust boundedness/decay for scalar waves at the Kerr Cauchy horizon in full range and sharp regularity.

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: Extends interior scalar wave theory beyond known regimes.

What remains open

Prove robust boundedness/decay for scalar waves at the Kerr Cauchy horizon in full range and sharp regularity.

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-611 — Prove generic Lipschitz (or C1) inextendibility of near-Kerr MGHDs.
• 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-615 — Show that small vacuum perturbations of Kerr produce weak null singularities generically at the Cauchy horizon.

Editorial / maintainer notes

Source manifest: N-054 (expansion_from_manifest.tsv). Numeric footnotes from the original table are not reproduced in this repository.