Prove analogous Cauchy-horizon instability results for coupled gravito-electromagnetic perturbations on Kerr-Newman.

Summary

Prove analogous Cauchy-horizon instability results for coupled gravito-electromagnetic perturbations on Kerr-Newman.

Why this matters

Needed for SCC and stability in charged rotating interiors.

Exact scope

Background / setting

Kerr–Newman interior / Cauchy-horizon regime for the Einstein–Maxwell system.

Equation type

PDE level: einstein-maxwell, 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–Newman parameters; state charge, angular-momentum, and proximity-to-extremality windows.

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

Theorem status follows literature as summarized in known results and references (not upgraded without verified solution pointers).

Problem statement

Prove analogous Cauchy-horizon instability results for coupled gravito-electromagnetic perturbations on Kerr-Newman.

What is already known

• Nonlinear stability of vacuum Kerr is proved for sufficiently small $|a|/M$ (Klainerman–Szeftel).
  Regime: Nonlinear Einstein vacuum, asymptotically flat, small angular momentum per unit mass.
  Strongest unconditional nonlinear theorem toward the full subextremal conjecture.
• Linearized Teukolsky/wave decay and mode stability on fixed subextremal Kerr are developed in depth (microlocal and physical-space methods).
  Regime: Linearized gravity and scalar waves on exact Kerr.
  Standard toolbox; not equivalent to nonlinear stability for all parameters.
• Sharp Price-law exponents and nonlinear tail matching are understood in restricted settings (e.g. linearized models, Schwarzschild); sharp nonlinear Kerr curvature tails are not settled.
  Regime: Late-time asymptotics; mixed linear vs nonlinear literature.
  Locates what “sharp Price law” demands beyond integrated decay.

Progress summary: Context: Needed for SCC and stability in charged rotating interiors.

What remains open

Prove analogous Cauchy-horizon instability results for coupled gravito-electromagnetic perturbations on Kerr-Newman.

Mathematical prerequisites

Match hypotheses to primary sources cited on this page; state minimal regularity, gauge class, and parameter windows in any claimed theorem.

Scope / taxonomy note

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 linear stability of weakly charged and slowly rotating Kerr-Newman family of charged black holes — He (2023)
  Linearized Einstein–Maxwell decay on weakly charged, slowly rotating Kerr–Newman; exterior input for interior instability problems.
• 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

Heuristic matches on family, cluster, equation level, asymptotics, and relevance.

• K-007 — Einstein–Maxwell stability near Kerr
• K-008 — Full asymptotically flat stability of the subextremal Kerr–Newman family
• K-308 — Rigidity and uniqueness with matter: full Kerr–Newman regime
• K-606 — Prove Kerr-Newman linear stability for a wider parameter regime beyond weak charge/slow rotation.
• K-607 — Prove nonlinear stability of Kerr-Newman in the asymptotically flat setting (full coupling).
• K-658 — Prove linear stability/instability classification for extremal Kerr-Newman under coupled perturbations.
• K-666 — Prove SCC threshold for Kerr-de Sitter and Kerr-Newman-de Sitter with explicit dependence on spectral gap.
• K-112 — Teukolsky interior asymptotics beyond the current state of the art

Editorial / maintainer notes

Source manifest: N-042 (expansion_from_manifest.tsv). Numeric footnotes from the original table are not reproduced in this repository.