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On the Stability of Anti-de Sitter Spacetime

Ali Nayeri·Tuan Tran
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Abstract

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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Ali Nayeri, Tuan Tran. 2004-12-27. On the Stability of Anti-de Sitter Spacetime. https://arxiv.org/abs/hep-th/0412304

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