Black hole instabilities and local Penrose inequalities

TL;DR

This paper introduces a method using local Penrose inequalities to identify instabilities in higher-dimensional black holes, confirming known instabilities and discovering new ones like fat black ring instability.

Contribution

It presents a simplified approach to detect black hole instabilities via initial data violating Penrose inequalities, applicable to various black hole configurations.

Findings

Black string initial data violate inequalities at Gregory-Laflamme instability points.

Confirmed ultraspinning instability in Myers-Perry black holes.

Fat black rings are unstable, thin rings show no symmetric instability.

Abstract

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.