Global nonlinear stability of the full subextremal Kerr family

Prove global nonlinear stability for the full subextremal range of Kerr black holes in general relativity by showing that small perturbations of initial data for a subextremal Kerr solution evolve into metrics that decay to a nearby Kerr solution for all future times.

Background

Within their survey of stability results in general relativity, the authors recall that while major progress has been made—such as linear stability of Schwarzschild, nonlinear stability of slowly rotating Kerr, and linear stability in the full subextremal regime—the global nonlinear stability for the entire subextremal Kerr family remains unresolved.

This problem is central to the black hole stability program and serves as a benchmark for understanding the long-time dynamics of perturbations of rotating black holes.