Spectroscopy of Kerr-AdS${}_5$ spacetime with the Heun function: Quasinormal modes, greybody factor, and evaporation

Abstract

We investigate quasinormal modes, greybody factor, and Hawking evaporation of a five-dimensional Kerr-anti de Sitter (AdS${}_5$) black hole by solving a wave equation for a test massive scalar field in terms of the local Heun function. We clarify the distribution of the quasinormal modes satisfying the ingoing and decaying boundary conditions at the event horizon and conformal infinity, respectively, and their splitting behaviors in the complex frequency plane with respect to a variation of spin parameters. We also point out the existence of purely imaginary modes. Further, we develop a method to extract in/outgoing waves near the AdS boundary, which enables us to define the greybody factor for a wide range of parameter space complementary to previous works. Using the greybody factor, we compute evaporation rates for mass and spins for the Kerr-AdS${}_5$ black hole via the Hawking radiation of the scalar field.

25 pages, 17 figures , Matches published version in PRD

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• Charged massless scalar fields in a charged $C$-metric black hole: Exact solutions, Hawking radiation, and scattering of scalar waves
• Revisiting PBH accretion, evaporation and their cosmological consequences
• The scalar angular Teukolsky equation and its solution for the Taub-NUT spacetime
• Investigation of hidden symmetry in $Ad{S}_5$ black hole with Heun equation