We revisit the quasinormal-mode and greybody factor correspondence for Kerr black holes in the eikonal limit and develop a systematic Wentzel–Kramers–Brillouin (WKB)-based formulation by recasting the radial Teukolsky equation into a Schrödinger-type equation with a short-range potential. Building on earlier studies of the correspondence in rotating backgrounds, we extend the analysis to gravitational perturbations and incorporate higher-order WKB corrections beyond the leading eikonal approximation. For gravitational perturbations, the predicted greybody factors are in good agreement with numerical results obtained from the generalized Sasaki-Nakamura equation, with increasing accuracy at large angular quantum number. We also identify the breakdown of the correspondence in the superradiant regime, where the WKB assumptions cease to be valid.

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• Classical black holes
• Gravitational waves