Eigenvalue repulsions in the quasinormal spectra of the Kerr-Newman black hole

We study the gravito-electromagnetic perturbations of the Kerr-Newman (KN) black hole metric and identify the two $-$ photon sphere and near-horizon $-$ families of quasinormal modes (QNMs) of the KN black hole, computing the frequency spectra (for all the KN parameter space) of the modes with the slowest decay rate. We uncover a novel phenomenon for QNMs that is unique to the KN system, namely eigenvalue repulsion between QNM families. Such a feature is common in solid state physics where \eg it is responsible for energy bands/gaps in the spectra of electrons moving in certain Schr\"odinger potentials. Exploiting the enhanced symmetries of the near-horizon limit of the near-extremal KN geometry we also develop a matching asymptotic expansion that allows us to solve the perturbation problem using separation of variables and provides an excellent approximation to the KN QNM spectra near extremality. The KN QNM spectra here derived are required not only to account for the gravitational emission in astrophysical environments, such as the ones probed by LIGO, Virgo and LISA, but also allow to extract observational implications on several new physics scenarios, such as mini-charged dark-matter or certain modified theories of gravity, degenerate with the KN solution at the scales of binary mergers.