Scalar QNM spectra of Kerr and Reissner-Nordström revealed by eigenvalue repulsions in Kerr-Newman
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jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pRecent studies of the gravito-electromagnetic frequency spectra of Kerr-Newman (KN) black holes have revealed two families of quasinormal modes (QNMs), namely jats:italicphoton sphere</jats:italic> modes and jats:italicnear-horizon</jats:italic> modes. However, they can only be unambiguously distinguished in the Reissner-Nordström (RN) limit, due to a phenomenon called jats:italiceigenvalue repulsion</jats:italic> (also known as jats:italiclevel repulsion</jats:italic>, jats:italicavoided crossing</jats:italic> or the jats:italicWigner-Teller effect</jats:italic>), whereby the two families can interact strongly near extremality. We find that these features are also present in the QNM spectra of a scalar field in KN, where the perturbation modes are described by ODEs and thus easier to explore. Starting from the RN limit, we study how the scalar QNM spectra of KN dramatically changes as we vary the ratio of charge to angular momentum, all the way until the Kerr limit, while staying at a fixed distance from extremality. This scalar field case clarifies the (so far puzzling) relationship between the QNM spectra of RN and Kerr black holes and the nature of the eigenvalue repulsions in KN, that ultimately settle the fate of the QNM spectra in Kerr. We study not just the slowest-decaying QNMs (both for jats:italicℓ</jats:italic> = jats:italicm</jats:italic> = 0 and jats:italicℓ</jats:italic> = jats:italicm</jats:italic> = 2), but several sub-dominant overtones as well, as these turn out to play a crucial role understanding the KN QNM spectra. We also give a new high-order WKB expansion of KN QNMs that typically describes the photon sphere modes beyond the eikonal limit, and use a matched asymptotic expansion to get a very good approximation of the near-horizon modes near extremality.</jats:p>
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Acknowledgements: The authors acknowledge the use of the IRIDIS High Performance Computing Facility, and associated support services at the University of Southampton, in the completion of this work. O. J. C. D. acknowledges financial support from the STFC “Particle Physics Grants Panel (PPGP) 2018” Grant No. ST/T000775/1. J. E. S. has been partially supported by STFC consolidated grants ST/P000681/1, ST/T000694/1. The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement no. [247252].
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1029-8479
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Science and Technology Facilities Council (ST/P000681/1)
STFC (ST/T000694/1)
Science and Technology Facilities Council (ST/P000673/1)