Analytic formula for quasinormal modes in the near-extreme Kerr-Newman-de Sitter spacetime governed by a non-P\"oschl-Teller potential

TL;DR

This paper derives an analytical formula for quasinormal modes in near-extreme Kerr-Newman-de Sitter spacetime, covering scalar, electromagnetic, gravitational, and fermionic fields, extending previous results to more general black hole configurations.

Contribution

It provides the first analytical expressions for quasinormal modes of fermionic fields and extends these formulas to charged rotating black holes in near-extreme Kerr-Newman-de Sitter spacetime.

Findings

Analytical formulas for quasinormal frequencies of various fields in near-extreme Schwarzschild-de Sitter black holes.

Extension of these formulas to Kerr-Newman-de Sitter black holes with charge and rotation.

Fermionic fields do not lead to Pöschl-Teller potential but still have analytically obtainable quasinormal modes.

Abstract

Quasinormal modes of scalar, electromagnetic, and gravitational fields in the extreme Schwarzschild-de Sitter background are known to be expressed in analytic form as eigenvalues of the P\"oschl-Teller wavelike equation. We show that perturbations of fermionic fields (given by Dirac and Rarita-Schwinger equations) do not lead to the P\"oschl-Teller effective potential. Nevertheless, using the Frobenius method we find quasinormal modes analytically in this case as well. We write down the analytical formula for quasinormal frequencies of the near-extreme Schwarzschild-de Sitter black holes, which is valid for both bosonic and fermionic fields. We further extend the analysis to the case of charged rotating black holes and find a general analytical formula for quasinormal modes of the fields of various spin for the near extreme Kerr-Newman-de Sitter spacetime.