Black Hole Quasinormal Modes and Seiberg-Witten Theory

TL;DR

This paper establishes a novel analytic connection between black hole quasinormal modes and four-dimensional supersymmetric gauge theories, providing exact quantization conditions and eigenvalue formulas validated against numerical results.

Contribution

It introduces an exact Bohr-Sommerfeld quantization framework for quasinormal modes using Nekrasov partition functions, linking black hole physics with supersymmetric gauge theory.

Findings

Derived exact quantization conditions for quasinormal modes.

Obtained explicit eigenvalue formulas for spheroidal harmonics.

Validated results against numerical computations for Kerr and Schwarzschild black holes.

Abstract

We present new analytic results on black hole perturbation theory. Our results are based on a novel relation to four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories. We propose an exact version of Bohr-Sommerfeld quantization conditions on quasinormal mode frequencies in terms of the Nekrasov partition function in a particular phase of the $\Omega$-background. Our quantization conditions also enable us to find exact expressions of eigenvalues of spin-weighted spheroidal harmonics. We test the validity of our conjecture by comparing against known numerical results for Kerr black holes as well as for Schwarzschild black holes. Some extensions are also discussed.