Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-09-06
Phys.Rev.D82:126013,2010
Physics
High Energy Physics
High Energy Physics - Theory
23 pages; references added; typos corrected, more clarifications, published version
Scientific paper
10.1103/PhysRevD.82.126013
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.
Chen Bin
Long Jiang
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