An alternative to the Teukolsky equation

Abstract

We conjecture a new ordinary differential equation exactly isospectral to the radial component of the homogeneous Teukolsky equation. We find this novel relation by a hidden symmetry implied from a four-dimensional $\mathcal{N}=2$ supersymmetric quantum chromodynamics. Our proposal is powerful both in analytical and in numerical studies. As an application, we derive high-order perturbative series of quasinormal mode frequencies in the slowly rotating limit. We also test our result numerically by comparing it with a known technique.