Instability of higher dimensional extreme black holes

TL;DR

This work analyzes linearized perturbations of vacuum extreme black holes in any dimension using the GHP formalism, revealing a horizon-local mechanism for instability via zero modes of horizon operators ${\mathcal A}_s$. By deriving decoupled or near-decoupled horizon equations for scalar, electromagnetic, and gravitational perturbations, the authors construct conserved horizon quantities $I_s$ whose nonzero values imply non-decay of horizon data and, for gravitational perturbations in algebraically special backgrounds, linear growth of certain radial derivatives. The key finding is a unifying instability criterion: axisymmetric zero modes of ${\mathcal A}_s$ with nonzero horizon charge render perturbations non-decaying (and in gravity, blow-up of $\partial_r\tilde{\Omega}_{ij}$), with concrete evidence in higher-dimensional extreme Myers–Perry black holes, including all 5D cases. This power-law instability complements earlier BF-bound analyses and informs the understanding of horizon dynamics, backreaction, and the endpoint of such perturbations in higher 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.