Spyros Alexakis (Toronto)

Title: Singularity formation in Black Hole interiors
Abstract: The prediction that solutions of the Einstein equations in the interior of black holes must always terminate at a singularity was originally conceived by Penrose in 1969, under the name of "strong cosmic censorship hypothesis". The nature of this break-down (i.e. the asymptotic properties of the space-time metric as one approaches the terminal singularity) is not predicted, and remains a hotly debated question to this day. One key question is the causal nature of the singularity (space-like, vs null for example). Another is the rate of blow-up of natural physical/geometric quantities at the singularity. Mutually contradicting predictions abound in this topic. Much work has been done under the assumption of spherical symmetry (for various matter models). We present a stability result for the Schwarzschild singularity under polarized axi-symmetric perturbations of the initial data, joint with G. Fournodavlos). One key innovation of our approach is a certain new way to treat the Einstein equations in axial symmetry, which should have broader applicability.