Quasinormal modes for a Kerr-de Sitter black hole in the eikonal limit and a generalization to Myers–Perry-de Sitter black holes with a single rotation

In this paper, the quasi-normal modes for a Kerr-de Sitter black hole in the geometric optics limit (“photon sphere” quasi-normal modes) for both corotating and counterrotating orbits are studied by calculating the Lyapunov exponent and other relevant parameters. After that, a generalization is made to the case of higher dimensional Kerr-de Sitter black holes-Myers–Perry-de Sitter black holes with a single rotation. The behavior of the parameters is examined for different values of the ratio of specific angular momentum and mass in higher dimensions. The obtained results are also compared with the already established findings in other well-known cases such as Schwarzschild, Schwarzschild-de Sitter, Kerr, and Kerr-de Sitter black holes. It is seen that there is complete agreement between them. Furthermore, the approximation here is accurate even when the eikonal limit is not strictly followed, especially in the slow rotation limit.