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.

在本文中，通过计算李雅普诺夫指数和其他相关参数，研究了同向和反向旋转轨道的几何光学极限（“光子球”准正常模式）的克尔德西特黑洞的准正常模式。之后，对单次旋转的高维 Kerr-de Sitter 黑洞-Myers-Perry-de Sitter 黑洞的情况进行了推广。针对更高维度中特定角动量和质量的比率的不同值检查参数的行为。获得的结果也与其他众所周知的案例中已经确定的发现进行了比较，例如 Schwarzschild、Schwarzschild-de Sitter、Kerr 和 Kerr-de Sitter 黑洞。可见他们之间完全一致。此外，