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

TL;DR

This paper analyzes quasinormal modes, greybody factors, and evaporation of a five-dimensional Kerr-AdS black hole using Heun functions, revealing mode behaviors and calculating Hawking radiation effects.

Contribution

It introduces a method to solve wave equations with Heun functions for Kerr-AdS$_5$ black holes, providing new insights into mode distributions and evaporation rates.

Findings

Identification of quasinormal mode distributions and splitting behaviors.

Development of a method to extract in/outgoing waves near the AdS boundary.

Calculation of evaporation rates via greybody factors for Kerr-AdS$_5$ black holes.

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.