Hidden Conformal Symmetry and Quasi-normal Modes

Abstract

We provide an algebraic way to calculate the quasi-normal modes of a black hole, which possesses a hidden conformal symmetry. We construct an infinite tower of quasi-normal modes from the highest-weight mode, in a simple and elegant way. For the scalar, the hidden conformal symmetry manifest itself in the fact that the scalar Laplacian could be rewritten in terms of the $SL(2,R)$ quadratic Casimir. For the vector and the tensor, the hidden conformal symmetry acts on them through Lie derivatives. We show that for three-dimensional black holes, with appropriate combination of the components the radial equations of the vector and the tensor could be written in terms of the Lie-induced quadratic Casimir. This allows the algebraic construction of the quasi-normal modes feasible. Our results are in good agreement with the previous study.

23 pages; references added; typos corrected, more clarifications, published version

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Cited by in corpus (6)

• Hidden Conformal Symmetry of Self-Dual Warped AdS_3 Black Holes in Topological Massive Gravity
• Quasinormal Modes of Self-Dual Warped AdS${}_3$ Black Hole in Topological Massive Gravity
• Quasi-normal Modes of Extremal Black Holes from Hidden Conformal Symmetry
• On hidden symmetries of extremal Kerr-NUT-AdS-dS black holes
• Scaling dimensions in hidden Kerr/CFT
• $SL(2,R)$ symmetry and quasi-normal modes in the BTZ black hole