Four proofs of Cauchy horizon instability
The theory of general relativity is known to be locally deterministic. However, it is not globally deterministic in particular because of smooth "Cauchy horizons" in the interior of black holes. Nonetheless, these smooth Cauchy horizons are expected to be unstable so that one can still hope that determinism is restored generically. I will explain the story from the beginning and discuss four different ways to prove this instability using ideas from analysis, geometry, scattering theory and number theory. I will try to explain the physical situation for which each proof is relevant.