Kerr-Newman quasinormal modes and Seiberg-Witten theory

TL;DR

This paper investigates the connection between Kerr-Newman black hole quasinormal modes and Seiberg-Witten theory, providing numerical evidence for the conjecture's validity in certain regimes and deriving a simplified isospectral equation.

Contribution

It clarifies the conjecture relating black hole quasinormal modes to Seiberg-Witten theory and tests it for Kerr-Newman black holes in the Dudley-Finley approximation, extending previous work.

Findings

Numerical evidence supports the conjecture for subextremal black holes.

The slowest damped quasinormal frequencies align with the conjecture.

Derived a simple isospectral radial equation using supersymmetric symmetries.

Abstract

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.