Prove Kerr-Newman linear stability for a wider parameter regime beyond weak charge/slow rotation.
Summary
Prove Kerr-Newman linear stability for a wider parameter regime beyond weak charge/slow rotation.
Why this matters
Extends Einstein-Maxwell stability program toward the full family.
Exact scope
- Background / setting
- asymptotically flat 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 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
Prove Kerr-Newman linear stability for a wider parameter regime beyond weak charge/slow rotation.
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 Einstein-Maxwell stability program toward the full family.
What remains open
Prove Kerr-Newman linear stability for a wider parameter regime beyond weak charge/slow rotation.
Parent problem
- K-008 — Full asymptotically flat stability of the subextremal Kerr–Newman family
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 Linear stability of slowly rotating Kerr–Newman black holes — Hung, Kellerbauer, Luk (2023) Linearized Einstein–Maxwell decay on weakly charged, slowly rotating Kerr–Newman.
- 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-607 — Prove nonlinear stability of Kerr-Newman in the asymptotically flat setting (full coupling).
- K-007 — Einstein–Maxwell stability near Kerr
- K-008 — Full asymptotically flat stability of the subextremal Kerr–Newman family
- K-642 — Prove analogous Cauchy-horizon instability results for coupled gravito-electromagnetic perturbations on Kerr-Newman.
- K-658 — Prove linear stability/instability classification for extremal Kerr-Newman under coupled perturbations.
- K-308 — Rigidity and uniqueness with matter: full Kerr–Newman regime
- K-601 — Prove unconditional linear stability of Kerr (full subextremal range) in a fixed gauge, with full decay rates.
- K-602 — Prove nonlinear stability of Kerr for the full subextremal range |a|<M.
Editorial / maintainer notes
Deduplicated from the main index by the 2026-06-03 audit. Track this as a subproblem or alias of K-008.
Source manifest: N-006 (expansion_from_manifest.tsv). Numeric footnotes from the original table are not reproduced in this repository.