  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.
