Linear Mode Stability of the Kerr-Newman Black Hole and Its Quasinormal Modes

Campos Dias, Oscar, Godazgar, Mahdi and Santos, Jorge E. (2015) Linear Mode Stability of the Kerr-Newman Black Hole and Its Quasinormal Modes. Physical Review Letters, 114, [151101]. (doi:10.1103/PhysRevLett.114.151101).

Abstract

We provide strong evidence that, up to 99.999% of extremality, Kerr-Newman black holes (KN BHs) are linear mode stable within Einstein-Maxwell theory. We derive and solve, numerically, a coupled system of two PDEs for two gauge invariant fields that describe the most general linear perturbations of a KN BH (except for trivial modes that shift the parameters of the solution). We determine the quasinormal mode (QNM) spectrum of the KN BH as a function of its three
parameters and find no unstable modes. In addition, we find that the QNMs that are connected continuously to the gravitational l = m = 2 Schwarzschild QNM dominate the spectrum for all values of the parameter space (m is the azimuthal number of the wave function and l measures the number of nodes along the polar direction). Furthermore, all QNMs with l = m approach Re ω = mΩext and Im ω = 0 at extremality; this is a universal property for any field of arbitrary H
spin |s| ≤ 2 propagating on a KN BH background (ω is the wave frequency and Ωext the BH angular velocity at extremality). We compare our results with available perturbative results in the small charge or small rotation regimes and find good agreement. We also present a simple proof that the Regge-Wheeler (odd) and Zerilli (even) sectors of Schwarzschild perturbations must be isospectral.

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Contributors

Author: Oscar Campos Dias

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