Abstract
We provide an algebraic way to calculate the quasinormal modes of a black hole, which possesses a hidden conformal symmetry. We construct an infinite tower of quasinormal modes from the highest-weight mode, in a simple and elegant way. For the scalar, the hidden conformal symmetry manifests itself in the fact that the scalar Laplacian could be rewritten in terms of the 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 an 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 makes the algebraic construction of the quasinormal modes feasible. Our results are in good agreement with the previous study.
- Received 2 November 2010
DOI:https://doi.org/10.1103/PhysRevD.82.126013
© 2010 The American Physical Society