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Damped and zero-damped quasinormal modes of charged, nearly extremal black holes

Zimmerman, Aaron and Mark, Zachary (2016) Damped and zero-damped quasinormal modes of charged, nearly extremal black holes. Physical Review D, 93 (4). Art. No. 044033. ISSN 2470-0010. doi:10.1103/PhysRevD.93.044033.

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Despite recent progress, the complete understanding of the perturbations of charged, rotating black holes as described by the Kerr-Newman metric remains an open and fundamental problem in relativity. In this study, we explore the existence of families of quasinormal modes of Kerr-Newman black holes whose decay rates limit to zero at extremality, called zero-damped modes in past studies. We review the nearly extremal and WKB approximation methods for spin-weighted scalar fields (governed by the Dudley-Finley equation) and give an accounting of the regimes where scalar zero-damped and damped modes exist. Using Leaver’s continued fraction method, we verify that these approximations give accurate predictions for the frequencies in their regimes of validity. In the nonrotating limit, we argue that gravito-electromagnetic perturbations of nearly extremal Reissner-Nordström black holes have zero-damped modes in addition to the well-known spectrum of damped modes. We provide an analytic formula for the frequencies of these modes, verify their existence using a numerical search, and demonstrate the accuracy of our formula. These results, along with recent numerical studies, point to the existence of a simple universal equation for the frequencies of zero-damped gravito-electromagnetic modes of Kerr-Newman black holes, whose precise form remains an open question.

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Additional Information:© 2016 American Physical Society. Received 10 December 2015; published 11 February 2016. We thank Emanuele Berti, Yanbei Chen, David Nichols, Huan Yang, Anıl Zenginoğlu and Fan Zhang for previous collaboration and valuable discussion on the topic of the QNMs of nearly extremal black holes. We are especially grateful to Huan Yang and Yanbei Chen for collaboration on additional studies of Kerr-Newman black holes and the WKB approximation for QNMs, which this study grew out of, and to Yanbei Chen and Fan Zhang for past collaboration on the implementation of Leaver’s method in the Kerr spacetime. We also thank Sam Gralla and Alexandru Lupsasca for insights into the near-horizon region of nearly extremal Kerr. A. Z. was supported by the Beatrice and Vincent Tremaine Postdoctoral Fellowship at the Canadian Institute for Theoretical Astrophysics during much of this work. Z. M. is supported by NSF Grant No. PHY-1404569, CAREER Grant No. 0956189, the David and Barbara Groce Startup Fund at Caltech, and the Brinson Foundation. A portion of this work was carried out at the Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the government of Canada and by the Province of Ontario though Ministry of Research and Innovation.
Funding AgencyGrant Number
Canadian Institute for Theoretical AstrophysicsUNSPECIFIED
Caltech David and Barbara Groce Startup FundUNSPECIFIED
Brinson FoundationUNSPECIFIED
Government of CanadaUNSPECIFIED
Province of Ontario Ministry of Research and InnovationUNSPECIFIED
Issue or Number:4
Record Number:CaltechAUTHORS:20160303-134915254
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Official Citation:Damped and zero-damped quasinormal modes of charged, nearly extremal black holes Aaron Zimmerman and Zachary Mark Phys. Rev. D 93, 044033 – Published 11 February 2016
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:65029
Deposited By: Tony Diaz
Deposited On:04 Mar 2016 20:57
Last Modified:10 Nov 2021 23:38

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