K-011

Spin fields on dynamical near-Kerr backgrounds

partial Exterior Stability

Statement

Prove robust decay and Morawetz estimates for spin 1 and spin 2 fields on time-dependent metrics that stay close to Kerr within a nonlinear bootstrap regime.

Mathematical prerequisites

Physical-space decay without exact separability; perturbative microlocal analysis; nonstationary commutator methods.

Why it matters

Nonlinear Einstein proofs require estimates on fields propagating on dynamical, not exactly stationary, backgrounds.

Completion criteria

A complete answer must give coercive estimates compatible with nonlinear closure and quantify all losses due to the time-dependent background.

Implications if solved

Would remove a major technical bottleneck between linear theory and a full nonlinear Kerr theorem.

Last updated: 2026-04-05 · Edit on GitHub →