Description
Quasinormal modes (QNMs) describe the characteristic oscillations of black holes and play an important role in observations of the ringdown phase. These modes are determined by the effective potential in the master equation for gravitational perturbations, raising the question of to what extent the potential can be uniquely determined from the QNM spectrum. In this talk, we explore this question using Darboux transformations of the wave function. We examine under what conditions Darboux transformations yield physically reasonable effective potentials. We also discuss the implications of these transformations for interpreting black hole QNM spectra.
