Nonlinear codimension-1 stability of extremal Kerr with horizon hair

open Extremal / Near-Extremal

Statement

Prove that a codimension-1 family of perturbations of extremal Kerr stays globally close to an extremal endstate while exhibiting Aretakis-type horizon growth in transversal derivatives.

Mathematical prerequisites

Degenerate horizon geometry; conserved charges; nonlinear modulation with reduced parameter freedom; null structure at κ=0.

Why it matters

Extremal Kerr is expected to be stable only in a codimension-1 sense, not in the same way as subextremal Kerr.

Completion criteria

A complete answer must identify the stable manifold, prove global exterior control, describe the final extremal parameters, and quantify the horizon growth.

Implications if solved

Would define the correct nonlinear stability statement for extremal rotating black holes.

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