At the centers of many galaxies lurk giant rotating black holes. Astrophysicists have long suspected that these objects are remarkably resilient: after swallowing a star or merging with another hole, they quickly settle down and forget the catastrophe. But proving this mathematically has eluded researchers for decades — the equations of curved spacetime are too complex.

This new work fills that gap. The author considered black holes of the Kerr family, those with mass and rotation, and proved that if you give them a slight 'nudge,' they won't be destroyed. The perturbation will dissipate like ripples from a stone thrown into a pond, and the hole will smoothly return to its previous shape. Only a tiny change remains: the mass and spin adjust to the kick. The decay rate is estimated as the inverse square of time — roughly like ripples that fade increasingly slowly but are guaranteed to vanish.

The mathematical trick resembles the work of a simultaneous interpreter. Instead of directly solving the equation for gravitational waves, the author introduces 'gauge corrections'—like an interpreter choosing words so the meaning isn't distorted. These corrections are sought together with the final parameters of the hole in a clever Nash–Moser iterative scheme. This bypasses the main difficulty: the impossibility of writing down the solution explicitly.

The result builds on two previous papers by the author. The first introduced a strong 'null condition'—a method that prevents errors from accumulating in calculations. The second provided estimates for wave equations with poor decay. Here they are assembled into a unified picture: a Kerr black hole is not a fragile crystal but an elastic ball that returns to its original shape after a blow.