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

Abstract The quasinormal modes of massless scalar field in rotating Bardeen and Hayward regular black holes are studied. The fundamental quasinormal modes and $$n=1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> first overtone quasinormal modes are calculated with the matrix method. Influences of model parameters on the quasinormal modes are also discussed. 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 $$g_*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mi>g</mml:mi> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> <mml:mrow/> </mml:mmultiscripts> </mml:math> . It is found that the monotonicity of fundamental and $$n=1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> quasinormal modes in the rotating Bardeen black hole is different. An interesting crossing phenomenon is also found for QNMs with different multipole numbers when we vary the parameter $$g_*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mi>g</mml:mi> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> <mml:mrow/> </mml:mmultiscripts> </mml:math> in the Bardeen case. 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.