Phase diagrams of quasinormal frequencies for Schwarzschild, Kerr, and Taub-NUT black holes

The Newman-Janis algorithm, which involves complex-coordinate transformations, establishes connections between static and spherically symmetric black holes and rotating and/or axially symmetric ones, such as between Schwarzschild black holes and Kerr black holes, and between Schwarzschild black holes and Taub-NUT black holes. However, the transformations in the two samples are based on different physical mechanisms. The former connection arises from the exponentiation of spin operators, while the latter from a duality operation. In this paper, we mainly investigate how the connections manifest in the dynamics of black holes. Specifically, we focus on studying the correlations of quasinormal frequencies among Schwarzschild, Kerr, and Taub-NUT black holes. This analysis allows us to explore the physics of complex-coordinate transformations in the spectrum of quasinormal frequencies.