K-005

Sharp nonlinear Price law for curvature

partial Exterior Stability

Statement

Prove optimal late-time inverse-power decay for gauge-invariant curvature quantities and relevant metric coefficients in nonlinear near-Kerr evolution.

Mathematical prerequisites

Sharp r^p hierarchies; resonance/low-frequency analysis; nonlinear bootstrap estimates; Bianchi equations; asymptotic mode coupling.

Why it matters

Sharp tails control how exterior decay feeds into interior instability and into the interpretation of ringdown signals.

Completion criteria

A complete answer must state exact exponents, identify generic nonvanishing leading coefficients, and prove matching upper and lower bounds.

Implications if solved

Would connect linear tail predictions to the full Einstein dynamics and feed directly into SCC formulations.

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