Gravitational instability in higher dimensions

Details Gravitational instability in higher dimensions Gravitational instability in higher dimensions

2002-06-21

arxiv.org/abs/hep-th/0206202v2

Phys.Rev.D66:064024,2002

Physics

High Energy Physics

High Energy Physics - Theory

1+43 pages. LaTeX. Slight rewording, typos fixed and stability of T^11 corrected

Scientific paper

10.1103/PhysRevD.66.064024

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''.

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