Endpoint of nonlinear evolution near extremality

Determine the eventual endpoint of the competition near extremality between long-lived, resonantly enhanced non-axisymmetric modes and spin-down through non-superradiant, particularly axisymmetric, channels in the nonlinear evolution of rapidly rotating Kerr black holes.

Background

Near-extremal Kerr black holes possess zero-damped quasinormal modes whose frequencies approach the superradiant bound. The paper explains that a quadratically generated (4,4) daughter mode can then lie close to a long-lived resonance, permitting weakly damped nonlinear perturbations to accumulate over long timescales.

This resonant growth competes with quadratic channels having axisymmetric m=0 content. Such modes do not benefit from superradiance and can be absorbed by the horizon; because they carry energy without axial angular momentum, their absorption tends to reduce the dimensionless spin and move the system away from resonance. The unresolved issue is the eventual outcome of this competition during nonlinear evolution.