Parametrized black hole quasinormal ringdown formalism for higher overtones

We investigate the parametrized black hole quasinormal ringdown formalism, which is a robust framework used to analyze quasinormal modes in systems that closely resemble general relativity, paying particular attention to the higher overtones. We find that larger deviations from the general relativity case typically appear in the quasinormal frequencies for the higher overtones. This growing tendency for higher overtones can be understood using an analytical method, and its relations to previous works are briefly discussed. Our findings indicate that we can impose a strong constraint on gravity theories by considering the overtones of quasinormal modes.