An alternative to the Teukolsky equation

TL;DR

This paper introduces a new isospectral ordinary differential equation related to the Teukolsky equation, derived from supersymmetric quantum chromodynamics, enabling improved analytical and numerical analysis of quasinormal modes.

Contribution

It proposes a novel isospectral ODE for the Teukolsky equation based on hidden supersymmetry, offering a new analytical tool for studying black hole perturbations.

Findings

Derived high-order perturbative series for quasinormal mode frequencies.

Validated the new approach through numerical comparisons.

Demonstrated analytical and numerical advantages of the new ODE.

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.