Gravitational instability in higher dimensions

TL;DR

This paper investigates classical gravitational instabilities in higher-dimensional spacetimes, deriving criteria for instability in various black hole and cosmological solutions, and exploring stabilization mechanisms and bubble stability.

Contribution

It provides new instability criteria based on the Lichnerowicz spectrum and analyzes stability of higher-dimensional bubbles and black strings.

Findings

Instability criterion for generalized black holes based on Lichnerowicz spectrum

Higher-dimensional bubbles of nothing can be unstable or stable depending on parameters

Embedding Ricci flat spacetimes into higher dimensions can stabilize perturbations

Abstract

We explore a classical instability of spacetimes of dimension $D>4$. Firstly, we consider static solutions: generalised black holes and brane world metrics. The dangerous mode is a tensor mode on an Einstein base manifold of dimension $D-2$. A criterion for instability is found for the generalised Schwarzschild, AdS-Schwarzschild and topological black hole spacetimes in terms of the Lichnerowicz spectrum on the base manifold. Secondly, we consider perturbations in time-dependent solutions: Generalised dS and AdS. Thirdly we show that, subject to the usual limitations of a linear analysis, any Ricci flat spacetime may be stabilised by embedding into a higher dimensional spacetime with cosmological constant. We apply our results to pure AdS black strings. Finally, we study the stability of higher dimensional ``bubbles of nothing''.