The Quasinormal Modes of Weakly Charged Kerr-Newman Spacetimes

TL;DR

This paper introduces a new perturbation theory-based method to calculate quasinormal modes of weakly charged Kerr-Newman black holes, indicating their stability and relevance to physics and astrophysics.

Contribution

A novel formalism extending quantum mechanics perturbation theory to compute quasinormal modes of Kerr-Newman black holes with weak charge.

Findings

No unstable modes found, suggesting stability.

Method applicable to non-square-integrable solutions.

Relevance to holography, general relativity, and astrophysics.

Abstract

The resonant mode spectrum of the Kerr-Newman spacetime is presently unknown. These modes, called the quasinormal modes, play a central role in determining the stability of Kerr-Newman black holes and their response to perturbations. We present a new formalism, generalized from time-independent perturbation theory in quantum mechanics, for calculating the quasinormal mode frequencies of weakly charged Kerr-Newman spacetimes of arbitrary spin. Our method makes use of an original technique for applying perturbation theory to zeroth-order solutions that are not square- integrable, and it can be applied to other problems in theoretical physics. The new formalism reveals no unstable modes, which together with previous results in the slow-rotation limit strongly indicates the modal stability of the Kerr-Newman spacetime. Our techniques and results are of interest in the areas of holographic duality, foundational problems in General Relativity, and possibly in astrophysical systems.