Description
The Kerr metrics model rotating vacuum black holes, and are expected to play a central role in the long-time description of generic solutions to the Einstein vacuum equation. They present the disturbing feature that determinism breaks down inside the black hole, beyond the Cauchy horizon. Penrose's Strong Cosmic Censorship conjecture states that this behavior is however unstable and vanishes upon small perturbations. I will present a recent work which proves that, assuming a non-linear Price's law-type estimate near the event horizon, in generic perturbations of Kerr black holes ruled by the full, non-linear, Einstein vacuum equation, a singularity forms at the Cauchy horizon near timelike infinity. This singularity - at the Lipschitz level for the metric - prevents the unphysical extensions and recovers determinism.