Analytical Forms and Degeneracy of Quasinormal Modes for Kerr-Newman-de Sitter Black Holes

TL;DR

This work derives analytic expressions for quasinormal mode (QNM) frequencies and radial wave functions of Kerr-Newman-de Sitter black holes for massless spin fields, showing the frequencies depend solely on black hole parameters and quantum numbers $n$ and $m$, and are independent of spin. By formulating a unified equation and reducing the radial problem to a Heun equation, the authors impose a polynomial (Heun) truncation to satisfy quasinormal boundary conditions, yielding the frequency $\omega = \frac{-i(n+1) + m\left(\frac{\Omega_{1}}{\kappa_{1}} + \frac{\Omega_{-1}}{\kappa_{-1}}\right)}{\frac{1}{\kappa_{1}} + \frac{1}{\kappa_{-1}}}$. While the frequencies are universal across spins, the radial wave function depends on a third quantum number $k$, giving a degeneracy of degree $n+1$ for each $(n,m)$. This establishes a theoretical basis for mimicking quasinormal modes across particle types and informs how QNM observations can constrain black hole parameters. Overall, the paper advances analytic QNM theory in KNdS spacetimes and reveals a rich structure of degeneracy and cross-spin equivalence.

Abstract

This study investigates the quasinormal modes of Kerr-Newman-de Sitter black holes for massless spin particles using the unified equation. We derive analytical expressions for both the quasinormal mode frequencies and the radial wave functions. The frequencies are determined exclusively by the black hole parameters and the quantum numbers $n$ and $m$, while the radial wave functions also depend on the quantum number $k$, indicating a degeneracy in frequency. For identical quantum numbers, the frequency expression and the degree of degeneracy are the same for all massless spin particles, regardless of their specific properties. This implies that, through the observation of quasinormal modes, one can not only determine the black hole's parameters but also observe the phenomenon in which one type of particle reproduces the quasinormal mode of another. Our work thus provides a theoretical foundation for understanding this mimicking behavior as well.