Abstract

Extremal Kerr black holes are members of the Kerr family of spacetimes that rotate at a maximum angular velocity. The goal of this talk is to shed some light on stability properties of extremal Kerr black holes and the nature of singularities in extremal black hole interiors by considering the simplified dynamical problem of the scalar wave equation on fixed Kerr backgrounds. It turns out that the behaviour of scalar fields on extremal black holes differs dramatically with their behaviour on more slowly rotating backgrounds. I will present recent instability results in the exterior of extremal black holes and their impact on late-time polynomial tails of the scalar field, which is joint work with Y. Angelopoulos and S. Aretakis. I will also discuss recent stability results on extremal black hole interiors, which show that in the context of scalar fields, the inner horizons in extremal black holes are less violent than in their more slowly rotating counterparts.