Nonlinear excitation of quasinormal modes for Kerr black holes

The excitation of a quadratic quasinormal mode is an important nonlinear phenomenon for a Kerr black hole ringing at a specific linear mode. The amplitude of this second-order effect is proportional to the square of the linear mode amplitude, with the ratio being linked to the nature of the Kerr black hole. We compute the dependency of this ratio on the dimensionless spin of the black hole, ranging up to 0.99. We find that the ratio does not vanish in the extremal limit. In this talk, I will go through two major steps of our calculation: (a) Analytically reconstructing the metric through the Chrzanowski, Cohen, and Kegeles approach (b) Numerically solving the second-order Teukolsky equation using the shooting method. As a byproduct, we find the Weyl scalars can be concisely expressed through the Hertz potential.