Scalar quasinormal modes, Lyapunov exponents and radii of null geodesics of rotating regular black holes

The quasinormal modes of massless scalar field in rotating Bardeen and Hayward regular black holes are studied. The fundamental quasinormal modes and $n=1$ first overtone quasinormal modes are calculated with two numerical methods, i.e. WKB method and matrix method. Impacts of model parameters on the quasinormal modes are also discussed. It is found that the quasinormal modes in rotating Hayward black hole have just percent-level increase compared with that in the Kerr black hole case due to the deviation parameter $g$, while there is ten-percent-level increase for the quasinormal modes in the rotating Bardeen black hole due to $g_*$. It is also found that the monotonicity of fundamental and $n=1$ quasinormal modes in the rotating Bardeen black hole is different. The corotating and counterrotating Lyapunov exponents of the equatorial null circular geodesics in the two rotating black holes are also calculated. Then, the connection between the imaginary parts and real parts of the eikonal quasinormal modes, particularly the first overtone ones, and the properties of the null geodesics in the two rotating regular black holes are explicitly verified.