Instability of higher dimensional extreme black holes

TL;DR

This paper investigates the stability of higher-dimensional extreme black holes by analyzing linearized gravitational perturbations, revealing conditions under which certain quantities diverge at the horizon, indicating potential instabilities.

Contribution

It demonstrates that perturbation equations can be decoupled at the horizon and identifies conditions leading to divergence, extending stability analysis to higher-dimensional extreme black holes.

Findings

Transverse derivatives of gauge-invariant quantities blow up at late times.

Conditions for divergence are satisfied by many extreme Myers-Perry black holes.

The analysis applies to black holes in any number of dimensions.

Abstract

We study linearized gravitational perturbations of extreme black hole solutions of the vacuum Einstein equation in any number of dimensions. We find that the equations governing such perturbations can be decoupled at the future event horizon. Using these equations, we show that transverse derivatives of certain gauge invariant quantities blow up at late time along the horizon if the black hole solution satisfies certain conditions. We find that these conditions are indeed satisfied by many extreme Myers-Perry solutions, including all such solutions in five dimensions.