Continuity of highly damped Kerr QNMs in the Schwarzschild limit

Establish whether the asymptotic (large-overtone) quasinormal-mode spectrum of Kerr black holes approaches the Schwarzschild spectrum continuously as the spin parameter a→0, and determine the mathematical and physical origin of the reported discontinuity between highly damped Kerr and Schwarzschild modes in this limit.

Background

Multiple studies reported that, contrary to expectations from spectral theory, the Kerr quasinormal-mode (QNM) spectrum in the high-damping limit seems not to tend continuously to the Schwarzschild spectrum as the rotation a→0. This led to the puzzle often summarized as “the spectrum of the limit is not the limit of the spectrum.”

This problem concerns the behavior of the QNM spectrum at large imaginary part (high overtones), where numerical and analytical methods have historically struggled, and clarifying the continuity limit is important both mathematically and physically for black-hole spectroscopy.