  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.
