I will present two results on the formation and the interior structure of black holes in general relativity.
The first result proves that extremal (zero temperature) black holes can form dynamically in gravitational collapse. This provides a definitive disproof of the ”third law of black hole thermodynamics.” This is joint work with Ryan Unger (Princeton).
The second result concerns black hole interiors and the Strong Cosmic Censorship conjecture due to Penrose. This conjecture asserts the deterministic character of general relativity. I will present work in the context of a negative cosmological constant that shows that whether determinism holds or not surprisingly depends on the Diophantine properties of the black hole geometry.