Classify superradiant instability windows for massive scalar fields on Kerr in fully rigorous parameter inequalities.
Summary
Classify superradiant instability windows for massive scalar fields on Kerr in fully rigorous parameter inequalities.
Why this matters
Turns existence into sharp parameter-domain characterization.
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 moduli $|a|<M$ (or stated KN/KdS extension); smallness measured in the stability topology on Cauchy data.
- 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
Classify superradiant instability windows for massive scalar fields on Kerr in fully rigorous parameter inequalities.
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: Turns existence into sharp parameter-domain characterization.
What remains open
Classify superradiant instability windows for massive scalar fields on Kerr in fully rigorous parameter inequalities.
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 Nonlinear stability of Kerr for small angular momentum (program) — Klainerman, Szeftel (2021) Theorem-level nonlinear stability of vacuum Kerr in a small $|a|/M$ regime; benchmark for full subextremal conjectures.
- survey Brief introduction to the nonlinear stability of Kerr — Klainerman, Szeftel (2022) Program overview, gauge structure, and relation between linear tools and nonlinear stability.
Related problems
Related by shared tags
- K-009 — Einstein–massive Klein–Gordon near Kerr: classification of stable and unstable regimes
- K-628 — Derive rigorous late-time tail constants for scalar wave on Kerr in full subextremal range.
- K-655 — Prove explicit sharp late-time asymptotics for scalar field along the event horizon in Kerr (full range).
- K-004 — Peeling and polyhomogeneous expansions at null infinity for nonlinear near-Kerr evolutions
- K-011 — Spin fields on dynamical near-Kerr backgrounds
- K-013 — Formation plus relaxation to Kerr
Editorial / maintainer notes
Source manifest: N-039 (expansion_from_manifest.tsv). Numeric footnotes from the original table are not reproduced in this repository.