Decades-old mystery in spinning black hole vibrations finally resolved

Rotating black holes ring down after perturbations in characteristic quasinormal modes, but near so-called algebraically special frequencies these modes behave erratically: they seem to split, vanish, or connect discontinuously to the non-rotating limit. By carefully tracking poles and zeros of the Green's function across multiple Riemann sheets, this work identifies two culprits—avoided crossings with resonant excitation explain the apparent bifurcations, while pole skipping (a quasinormal-mode pole cancelled by a Matsubara-mode zero) explains the disappearances. The result closes a puzzle that has persisted since the 1980s.