The Kerr stability conjecture — that rotating black holes are stable under small perturbations — has been proved for slowly rotating Kerr spacetimes. The full conjecture, covering all rotation rates up to the extremal limit, remains open. The gap is technical: the methods that work for slow rotation break down as the angular momentum increases.
The authors (arXiv:2603.23437) establish energy and Morawetz estimates for the Teukolsky equation — the master equation governing gravitational perturbations of Kerr — across the full subextremal range. The key innovations: a tensorial formulation based on a non-integrable approach, r-foliation-adapted microlocal multipliers, and a novel scalarization procedure that reduces tensorial wave problems to scalar ones.
These estimates control the growth of perturbation energy and ensure decay, which are the essential inputs for the nonlinear stability proof.
The through-claim: the obstacle to proving Kerr stability at high rotation rates is analytical, not physical. There's no evidence that rapidly rotating black holes are unstable — the estimates just need to be strong enough to close the nonlinear argument. This work provides those estimates, reducing the full stability conjecture to a matter of assembling existing techniques rather than discovering new ones.