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

Abstract

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 \cite{Zhang}. 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 $SL(2,R)\times U(1)$ isometry. To this end, we first introduce two associated tensor fields with the quadratic Casimir of $SL(2,R)\times U(1)$ 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 $SL(2,R)\times U(1)$ 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.

References updated, typos corrected, clarifications made, version to appear in JHEP

References in corpus (8)

• Warped AdS_3 Black Holes
• Black hole mass and angular momentum in topologically massive gravity
• Hidden Conformal Symmetry and Quasi-normal Modes
• Hidden conformal symmetry on the black hole photon sphere
• Self-Dual Warped AdS${}_3$ Black Holes
• 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
• $SL(2,R)$ symmetry and quasi-normal modes in the BTZ black hole