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

Published version
Peer-reviewed

Type

Article

Change log

Authors

Dias, Óscar JC 
Godazgar, Mahdi 
Santos, Jorge E 

Abstract

We provide strong evidence that, up to 99.999% of extremality, Kerr-Newman black holes (KNBHs) are linear mode stable within Einstein-Maxwell theory. We derive and solve, numerically, a coupled system of two partial differential equations for two gauge invariant fields that describe the most general linear perturbations of a KNBH. We determine the quasinormal mode (QNM) spectrum of the KNBH as a function of its three parameters and find no unstable modes. In addition, we find that the lowest radial overtone 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, the (lowest radial overtone) QNMs with ℓ=m approach Reω=mΩH(ext) and Imω=0 at extremality; this is a universal property for any field of arbitrary spin |s|≤2 propagating on a KNBH background (ω is the wave frequency and ΩH(ext) the black hole angular velocity at extremality). We compare our results with available perturbative results in the small charge or small rotation regimes and find good agreement.

Description

Keywords

gr-qc, gr-qc, astro-ph.HE, hep-th

Journal Title

Physical Review Letters

Conference Name

Journal ISSN

1079-7114
1079-7114

Volume Title

114

Publisher

American Physical Society
Sponsorship
Science and Technology Facilities Council (ST/J000434/1)
Science and Technology Facilities Council (ST/L000385/1)
Science and Technology Facilities Council (ST/L000636/1)
European Research Council (247252)
Some of the computations were performed at the cluster ‘BaltasarSete-Sóis’ and supported by the ERC Starting Grant No. DyBHo-256667. O. J. C. D. acknowledges the kind hospitality of the Yukawa Institute for Theoretical Physics, where part of this work has been done during the workshop “Holographic vistas on Gravity and Strings,” YITP-T-14-1. O. J. C. D. is supported by the STFC Ernest Rutherford Grants No. ST/K005391/1 and No. ST/M004147/1. M. G. is supported by King’s College, Cambridge. The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (No. FP7/ 2007-2013)/ERC Grant Agreement No. [247252].