K-002

Uniform nonlinear stability as a→M−

open Exterior Stability

Statement

Prove a version of Kerr stability whose constants and decay estimates remain uniform, or quantitatively controlled, as the spin approaches extremality.

Mathematical prerequisites

Degenerate redshift analysis; near-horizon scaling; semiclassical control near the photon region; uniform weighted energies in the surface-gravity parameter κ.

Why it matters

Near-extremal Kerr is the transition region between the standard subextremal theory and the qualitatively different extremal regime.

Completion criteria

A complete answer must track dependence on ε=1−|a|/M in all coercive estimates and separate unavoidable degeneracies from removable technical losses.

Implications if solved

Would bridge ordinary Kerr stability to extremal dynamics and sharpen what actually fails as κ→0.

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