On the Stability of Anti-de Sitter Spacetime

Details On the Stability of Anti-de Sitter Spacetime On the Stability of Anti-de Sitter Spacetime

2004-12-27

arxiv.org/abs/hep-th/0412304v1

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, no figure

Scientific paper

We present a detailed analysis for the classical stability of a four dimensional Anti-de Sitter spacetime (AdS$_4$) by decomposing the first-order perturbations of a spherical symmetric gravitational field into the so called tensor harmonics which transform as irreducible representative of the rotation group (Regge-Wheeler decomposition). It is shown that there is no nontrivial stationary perturbation for the angular momentum $l < 2$. The stability analysis forces the frequency of the gravitational modes to be constrained in a way that the frequency of scalar modes are constrained.

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