The ‘Strong Cosmic Censorship Conjecture' due to Roger Penrose is the mathematical statement that general relativity is a deterministic theory. I will present results on the linear version of the conjecture around the Kerr-Anti-de Sitter black hole.
It turns out that this is intimately tied to Diophantine properties of a suitable ratio of mass and angular momentum of the black hole and that the validity of the conjecture depends in an unexpected way on the notion of genericity imposed. The proof is based on precise quantitative estimates on the spectral measure in relevant phase space regions and in suitable semiclassical limits.