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 GregoryLaflamme instability appears. We then use the method to confirm the existence of the ultraspinning instability of MyersPerry 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.