An analysis of the quasinormal modes of Kerr-Newman black holes has identified 42 exceptional points at which pairs of modes coalesce in the non-Hermitian spectrum of these rotating and charged solutions. The work, based on the exact separated gravitoelectromagnetic equations, also clarifies how rotation and charge determine the relative excitation strengths of the different modes, an aspect previously little explored for black holes with simultaneous spin and charge.

Quasinormal modes describe the vibrations of a black hole after a perturbation, and their frequencies and damping rates depend on mass, spin, and charge. Excitation factors, which set the amplitude at which each mode is excited, are crucial for predicting the gravitational or electromagnetic signal associated. The study distinguishes gravitational-led and electromagnetic-led modes, analyzing how they evolve with spin at fixed charge.

The central result is that, at fixed charge, the magnitude of the excitation factor of gravitational-led modes decreases as spin increases, while electromagnetic-led modes show both monotonic and nonmonotonic behavior. A notable finding is that the first overtone can have an excitation factor comparable to or even larger than that of the fundamental mode, challenging the usual assumption that the fundamental mode always dominates the response. As for the exceptional points, some form sequences of successive overtone pairs that coalesce progressively closer to the extremal limit; the additional points outside these sequences share the same mode-pair labels, but occur at different values of spin and charge.

These results, obtained from the exact separated gravitoelectromagnetic equations of Kerr-Newman, provide a better understanding of how rotation and charge shape the modal structure of rotating, charged black holes. The identification of exceptional points in the non-Hermitian spectrum is relevant to the physics of open systems and to future gravitational-wave observations that could probe the region near the horizon of black holes with spin and charge.