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On quasi-normal modes and the AdS_5/CFT_4 correspondence

George Siopsis
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Abstract

We discuss the quasi-normal modes of massive scalar perturbations of black holes in AdS_5 in conjunction with the AdS/CFT correspondence. On the gravity side, we solve the wave equation and obtain an expression for the asymptotic form of quasi-normal frequencies. We then show that these expressions agree with those obtained from a CFT defined on $\mathbb{R} \times S^3$ in a certain scaling limit, by identifying Euclidean time with one of the periodic coordinates. This generalizes known exact results in three dimensions (BTZ black hole). As a by-product, we derive the standard energy quantization condition in AdS by a simple monodromy argument in complexified AdS space. This argument relies on an unphysical singularity.

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George Siopsis. 2005-03-16. On quasi-normal modes and the AdS_5/CFT_4 correspondence. https://doi.org/10.1016/j.nuclphysb.2005.03.023

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