Instability of charged and rotating naked singularities

TL;DR

This paper demonstrates that super-extremal black hole spacetimes with naked singularities are linearly unstable, suggesting they are unlikely to form as end states of gravitational collapse.

Contribution

It provides the first set of evidence, through exact and numerical solutions, that charged and rotating naked singularities are linearly unstable.

Findings

Unstable solutions exist for charged non-rotating cases.

Numerical evidence shows instability in rotating cases.

Results imply such naked singularities are unlikely physical endpoints.

Abstract

We provide evidence that ``super-extremal'' black hole space-times (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 space-times cannot be the endpoint of physical gravitational collapse.