Quasinormal modes of slowly rotating Kerr-Newman black holes using the double series method

TL;DR

This paper computes the quasinormal mode spectrum of slowly rotating Kerr-Newman black holes using a double series perturbative method, providing insights into their gravitational, electromagnetic, and scalar perturbations.

Contribution

It introduces a second-order perturbative double expansion method to analyze quasinormal modes of Kerr-Newman black holes, extending previous results to include slow rotation effects.

Findings

Reproduces known results for non-rotating cases.

Shows isospectrality between axial and polar perturbations is approximately valid.

Estimates quasinormal modes accurately up to 50-60% of extremal angular momentum.

Abstract

We calculate the spectrum of quasinormal modes of slowly rotating Kerr-Newman black holes. Using a perturbative double expansion method, second order in rotation and first order in non-radial perturbations, we obtain the system of equations that describe polar-led and axial-led perturbations. We analyse gravitational, electromagnetic and scalar fundamental modes, focusing on the $\mathrm{l}=2$ perturbations. We reproduce previous results and check that isospectrality between axial and polar-led perturbations is approximately satisfied with good accuracy. Our results show that the slow rotation approximation can be used to estimate with reasonable precision the spectrum of configurations up to 50-60$\%$ of the extremal angular momentum.