Instability of charged and rotating naked singularities

We provide evidence that “super-extremal” black hole spacetimes (either with charge larger than mass or angular momentum larger than mass), which contain naked singularities, are unstable under linearized perturbations. This is given by an infinite family of exact unstable solutions in the charged non-rotating case, and by a set of (unstable) numerical solutions in the rotating case. These results may be relevant to the expectation that these spacetimes cannot be the endpoint of physical gravitational collapse.