Black hole instabilities and local Penrose inequalities
Various higher-dimensional black holes have been shown to be unstable by studying linearized gravitational perturbations. This is often very complicated. I shall describe a simpler method for demonstrating instability. The idea is to construct initial data describing a small perturbation of the black hole and which violates an inequality analogous to the 4d Penrose inequality. I will describe recent work applying the method to non-uniform black strings.