Analytical forms and degeneracy of quasinormal modes for Kerr-Newman-de Sitter black holes

Black Hole and Gravitational Wave Group, Zhejiang University of Technology - Hangzhou 310023, China

Received: 27 November 2025
Accepted: 24 February 2026

Abstract

This study investigates the quasinormal modes of Kerr-Newman-de Sitter black holes for massless spin particles using the unified equation. Through the introduction of a new transformation and a newly developed analytical method, we rigorously derive the analytical expressions for the quasinormal mode frequencies and 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 holes 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.