Kerr-Newman quasinormal modes and Seiberg-Witten theory

It was recently suggested the quasinormal-mode spectrum of black holes is related to a class of four-dimensional $\mathcal{N}=2$ super Yang-Mills theories described by Seiberg-Witten curves, a proposal that has been tested for a number of black hole spacetimes. The aim of this study is to clarify the key ideas of this conjecture to a non-high-energy-physics audience and test it in a setting that has not yet been explored: the electromagnetic and gravitational perturbations of Kerr-Newman black holes in the Dudley-Finley approximation. In the parameter space we explore, we find numerical evidence that the conjecture is valid for subextremal black holes and its slowest damped quasinormal frequencies, thereby providing further support for the conjecture's validity. In addition, we exploit the symmetries of the four-dimensional $\mathcal{N}=2$ super Yang-Mills theory to obtain a strikingly simple isospectral version of the radial Dudley-Finley equation.