Mario Misas Arcos, Alberto T. Pérez, Carlos F. Sopuerta

Exceptional points (EPs) and eigenstate hysteresis, previously found in Kerr only with an auxiliary scalar field, arise intrinsically in the quasinormal-mode spectrum of Kerr-Newman black holes. Using a hyperboloidal formulation of the coupled gravito-electromagnetic Teukolsky equations and a Chebyshev pseudospectral method, we compute the $\ell=m=2$ spectrum and locate four EPs at up to $99.974\%$ of extremality, one from a new repulsion. The gaps close as a square root branch point, and quasistatic loops around one or more EPs exchange the coalescing modes, confirming hysteresis.