Gravitational instability in higher dimensions

We explore a classical instability of spacetimes of dimension $D>\mathrm{}4.\mathrm{}$ First, we consider static solutions: generalized 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 generalized 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: Generalized dS and AdS. Thirdly we show that, subject to the usual limitations of a linear analysis, any Ricci flat spacetime may be stabilized 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.”