Quasinormal modes of Kerr–de Sitter black holes

Abstract

We calculate the fundamental quasinormal modes of the Kerr--de Sitter black hole for the first time. In order to calculate the quasinormal modes, we employ the master equations derived by Suzuki, Takasugi, and Umetsu, who transform the Teukolsky equations for the Kerr--de Sitter black hole into the standard form of the Heun's equation. The transformed functions are expanded around the outer horizon of the black hole or the symmetric axis in the Fr\"obenius series whose coefficients satisfy a three-term recurrence relation. These three-term recurrence relations allow us to use Leaver's continued fraction method to calculate the angular separation constant and the quasinormal mode frequency. Any unstable fundamental quasinormal mode is not found in this paper. It is also observed that for some black holes characterized by a large mass parameter, some retrograde modes in the slow rotation limit become prograde as the black hole spin increases. This phenomenon does not occur for the fundamental modes of the Kerr black hole.