SL(2, R) × U(1) symmetry and quasinormal modes in the self-dual warped AdS black hole

Yuan Chen (Department of Physics, Beijing Normal University, Beijing, 100875, China) ; Wei Guo (Department of Physics, Beijing Normal University, Beijing, 100875, China) ; Kai Shi (Department of Physics, Beijing Normal University, Beijing, 100875, China) ; Hongbao Zhang (Department of Physics, Beijing Normal University, Beijing, 100875, China)

The algebraic approach to the spectrum of quasinormal modes has been made as simple as possible for the BTZ black hole by the strategy developed in [16]. By working with the self-dual warped AdS black hole, we demonstrate in an explicit way that such a strategy can be well adapted to those warped AdS balck holes with the SL(2, R) × U(1) isometry. To this end, we first introduce two associated tensor fields with the quadratic Casimir of SL(2, R) × U(1) Lie algebra in the self-dual warped AdS black hole and show that they correspond essentially to the metric and volume element up to a constant prefactor, respectively. Then without appealing to any concrete coordinate system, we can further show that the solutions to the equations of motion for the scalar, vector, spinor fields all fall into the representations of the SL(2, R) × U(1) Lie algebra by a purely abstract tensor and spinor analysis. Accordingly, the corresponding spectrum of quasinormal modes for each fixed azimuthal quantum number can be derived algebraically as the infinite tower of descendants of the highest weight mode of the SL(2, R) Lie subalgebra.

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      "source": "Springer", 
      "value": "The algebraic approach to the spectrum of quasinormal modes has been made as simple as possible for the BTZ black hole by the strategy developed in [16]. By working with the self-dual warped AdS black hole, we demonstrate in an explicit way that such a strategy can be well adapted to those warped AdS balck holes with the SL(2, R) \u00d7 U(1) isometry. To this end, we first introduce two associated tensor fields with the quadratic Casimir of SL(2, R) \u00d7 U(1) Lie algebra in the self-dual warped AdS black hole and show that they correspond essentially to the metric and volume element up to a constant prefactor, respectively. Then without appealing to any concrete coordinate system, we can further show that the solutions to the equations of motion for the scalar, vector, spinor fields all fall into the representations of the SL(2, R) \u00d7 U(1) Lie algebra by a purely abstract tensor and spinor analysis. Accordingly, the corresponding spectrum of quasinormal modes for each fixed azimuthal quantum number can be derived algebraically as the infinite tower of descendants of the highest weight mode of the SL(2, R) Lie subalgebra."
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Published on:
14 June 2023
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2023 (2023)
Issue 6
Pages 1-12
DOI:
https://doi.org/10.1007/JHEP06(2023)075
arXiv:
2303.11714
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: