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

References in corpus (38)

• The Black Hole in Three Dimensional Space Time
• Quasinormal modes of black holes and black branes
• Quasi-Normal Modes of Stars and Black Holes
• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Quasinormal Modes of AdS Black Holes and the Approach to Thermal Equilibrium
• Conformal Field Theory Interpretation of Black Hole Quasi-normal Modes
• Warped AdS_3 Black Holes
• Scalar, electromagnetic and Weyl perturbations of BTZ black holes: quasi normal modes
• Hidden Conformal Symmetry of the Kerr Black Hole
• Holographic Derivation of Kerr-Newman Scattering Amplitudes for General Charge and Spin
• Real-time correlators in Kerr/CFT correspondence
• Hidden Conformal Symmetry of the Kerr-Newman Black Hole
• Twofold Hidden Conformal Symmetries of the Kerr-Newman Black Hole
• Quasi-normal modes of warped black holes and warped AdS/CFT correspondence
• Hidden Conformal Symmetries of Five-Dimensional Black Holes
• Stability of warped AdS3 vacua of topologically massive gravity
• Entropy of Kaluza-Klein Black Hole from Kerr/CFT Correspondence
• Quasi-Normal Modes in Topologically Massive Gravity
• On Holographic description of the Kerr-Newman-AdS-dS black holes
• Hidden conformal symmetry of rotating charged black holes
• On Holographic Dual of the Dyonic Reissner-Nordström Black Hole
• Hidden Conformal Symmetry of the Reissner-Nordstrøm Black Holes
• Real-time Correlators and Hidden Conformal Symmetry in Kerr/CFT Correspondence
• Hidden Conformal Symmetry of Extremal Black Holes
• Hidden Conformal Symmetry of Kerr-Bolt Spacetimes
• Hidden conformal symmetry of extreme and non-extreme Einstein-Maxwell-Dilaton-Axion black holes
• Quasinormal modes of warped $Ad{S}_3$ black holes and AdS/CFT correspondence
• Hidden Conformal Symmetry of Self-Dual Warped AdS_3 Black Holes in Topological Massive Gravity
• Hidden Conformal Symmetry of Rotating Black Hole with four Charges
• Self-Dual Warped AdS${}_3$ Black Holes
• Black Hole Vacua and Rotation
• Zeta(n) via hyperbolic functions
• Notes on the Hidden Conformal Symmetry in the Near Horizon Geometry of the Kerr Black Hole
• Hidden Conformal Symmetry of Warped AdS_3 Black Holes
• Correlation Functions and Hidden Conformal Symmetry of Kerr Black Holes
• Quasinormal Modes of Self-Dual Warped AdS${}_3$ Black Hole in Topological Massive Gravity
• Hidden Conformal Symmetry of Rotating Black Holes in Minimal Five-Dimensional Gauged Supergravity
• Quasi-Normal Modes of Extremal BTZ Black Holes in TMG

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• Aspects of Warped AdS${}_3$/CFT${}_2$ Correspondence
• 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
• Photon Rings Around Warped Black Holes
• General Hidden Conformal Symmetry of 4D Kerr-Newman and 5D Kerr Black Holes
• Quasi-normal Modes of Extremal Black Holes from Hidden Conformal Symmetry
• Quasinormal modes of generalized Pöschl-Teller potentials
• Hidden conformal symmetry for the accelerating Kerr black holes
• On hidden symmetries of extremal Kerr-NUT-AdS-dS black holes
• Quasinormal Modes and Hidden Conformal Symmetry of Warped dS${}_3$ Black Hole
• Holographic description of three dimensional Godel black hole
• $SL(2,R)$ symmetry and quasi-normal modes in the BTZ black hole
• Scaling dimensions in hidden Kerr/CFT
• Quasinormal modes around the BTZ black hole at the tricritical generalized massive gravity
• On emergent conformal symmetry near the photon ring
• Gravitational Waves, Holography, and Black Hole Microstates
• $SL(2,R)\times U(1)$ symmetry and quasinormal modes in the self-dual warped AdS black hole
• Hidden conformal symmetries for black holes in modified gravity
• Harrison metrics for the Schwarzschild black hole
• Cosmology as a CFT${}_1$
• Quasinormal frequencies of a massless scalar in the hidden Kerr/CFT proposal
• Notes on Self-dual Warped dS${}_3$ Spacetime