Black hole instabilities and local Penrose inequalities

Various higher-dimensional black holes have been shown to be unstable by studying linearized gravitational perturbations. A simpler method for demonstrating instability is to find initial data that describes a small perturbation of the black hole and violates a Penrose inequality. An easy way to construct initial data is by conformal rescaling of the unperturbed black hole initial data. For a compactified black string, we construct initial data which violates the inequality almost exactly where the Gregory-Laflamme instability appears. We then use the method to confirm the existence of the 'ultraspinning' instability of Myers-Perry black holes. Finally, we study black rings. We show that 'fat' black rings are unstable. We find no evidence of any rotationally symmetric instability of 'thin' black rings.