Abstract

In order to gain a complete understanding of black holes in classical general relativity, we must first resolve both the issue of stability of the exterior region of Kerr black holes and the nature of the singularity in the interior of a perturbed Kerr black hole. The aim of this talk is to give an overview of some recent developments towards these issues, by considering the toy problem of a wave equation both outside and inside unperturbed Kerr black holes. In particular, I will highlight the geometric differences between subextremal and extremal Kerr, and describe how the analysis in the extremal limit suggests more instability in the exterior, yet more stability in the interior.