Nonlinear fate of Aretakis instability

open Extremal / Near-Extremal

Statement

Determine whether generic small perturbations of extremal Kerr settle to subextremal Kerr, remain extremal with horizon hair, or develop a stronger nonlinear instability.

Mathematical prerequisites

Nonlinear continuation near degenerate horizons; parameter drift; horizon-local blow-up criteria; conserved-charge dynamics.

Why it matters

The key physical question is whether the linear Aretakis effect survives, saturates, or resolves nonlinearly.

Completion criteria

A complete answer must prove one of the possible nonlinear outcomes for a generic class of perturbations and quantify the transition mechanism.

Implications if solved

Would tell us whether extremality is dynamically fragile or structurally persistent.

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