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

TL;DR

This paper derives analytical formulas for quasinormal modes of Kerr-Newman-de Sitter black holes, revealing degeneracies and particle-independent frequencies, which could help identify black hole parameters and particle effects through observations.

Contribution

It provides the first analytical expressions for quasinormal mode frequencies and wave functions, highlighting degeneracies and particle-independent features in Kerr-Newman-de Sitter black holes.

Findings

Derived analytical quasinormal mode frequencies and wave functions.

Identified degeneracy in frequencies depending on quantum number $k$.

Showed frequencies are independent of particle properties for given quantum numbers.

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.