Gravito-Electromagnetic Perturbations of Kerr-Newman Black Holes: Stability and Isospectrality in the Slow-Rotation Limit

TL;DR

This paper analyzes the stability and spectral properties of Kerr-Newman black holes under gravito-electromagnetic perturbations in the slow-rotation limit, providing new insights into their quasinormal modes and isospectrality.

Contribution

It introduces a method to compute quasinormal modes of Kerr-Newman black holes up to linear order in spin and demonstrates isospectrality between axial and polar sectors.

Findings

First fully-consistent stability analysis of Kerr-Newman black holes.

Quasinormal modes computed with 3% accuracy for moderate spins.

Evidence of isospectrality between axial and polar perturbations.

Abstract

The most general stationary black-hole solution of Einstein-Maxwell theory in vacuum is the Kerr-Newman metric, specified by three parameters: mass M, spin J and charge Q. Within classical general relativity, the most important and challenging open problem in black-hole perturbation theory is the study of gravitational and electromagnetic fields in the Kerr-Newman geometry, because of the indissoluble coupling of the perturbation functions. Here we circumvent this long-standing problem by working in the slow-rotation limit. We compute the quasinormal modes up to linear order in J for any value of Q and provide the first, fully-consistent stability analysis of the Kerr-Newman metric. For scalar perturbations the quasinormal modes can be computed exactly, and we demonstrate that the method is accurate within 3% for spins J/Jmax<~0.5, where Jmax is the maximum allowed spin for any value of Q. Quite remarkably, we find numerical evidence that the axial and polar sectors of the gravito-electromagnetic perturbations are isospectral to linear order in the spin. The extension of our results to nonasymptotically flat space-times could be useful in the context of gauge/gravity dualities and string theory.