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Quasinormal modes of nearly extremal Kerr spacetimes: Spectrum bifurcation and power-law ringdown

Yang, Huan and Zimmerman, Aaron and Zenginoğlu, Anıl and Zhang, Fan and Berti, Emanuele and Chen, Yanbei (2013) Quasinormal modes of nearly extremal Kerr spacetimes: Spectrum bifurcation and power-law ringdown. Physical Review D, 88 (4). Art. No. 044047. ISSN 2470-0010.

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We provide an in-depth investigation of quasinormal-mode oscillations of Kerr black holes with nearly extremal angular momenta. We first discuss in greater detail the two distinct types of quasinormal-mode frequencies presented in a recent paper [H. Yang et al., Phys. Rev. D 87 041502 (2013)]. One set of modes that we call “zero-damping modes” has vanishing imaginary part in the extremal limit and exists for all corotating perturbations (i.e. modes with azimuthal index m≥0). The other set (the “damped modes”) retains a finite decay rate even for extremal Kerr black holes and exists only for a subset of corotating modes. As the angular momentum approaches its extremal value, the frequency spectrum bifurcates into these two distinct branches when both types of modes are present. We discuss the physical reason for the mode branching by developing and using a bound-state formulation for the perturbations of generic Kerr black holes. We also numerically explore the specific case of the fundamental l=2 modes, which have the greatest astrophysical interest. Using the results of these investigations, we compute the quasinormal-mode response of a nearly extremal Kerr black hole to perturbations. We show that many superimposed overtones result in a slow power-law decay of the quasinormal ringing at early times, which later gives way to exponential decay. This exceptional early-time power-law decay implies that the ringdown phase is long lived for black holes with large angular momentum, which could provide a promising strong source for gravitational-wave detectors.

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Additional Information:© 2013 American Physical Society. Received 30 July 2013; published 26 August 2013. We thank David Nichols and Zhongyang Zhang for discussions during the early stages of this work and Sam Dolan for advice on the WKB method. This research is funded by NSF Grants No. PHY-1068881 and No. PHY- 1005655, CAREER Grants No. PHY-0956189 and No. PHY-1055103, NASA Grant No. NNX09AF97G, the Sherman Fairchild Foundation, the Brandon Foundation, and the David and Barbara Groce Startup Fund at Caltech.
Funding AgencyGrant Number
NSFPHY- 1005655
NSF CAREER GrantPHY-0956189
NSF CAREER GrantPHY-1055103
Sherman Fairchild FoundationUNSPECIFIED
Brandon FoundationUNSPECIFIED
David and Barbara Groce startup fund at CaltechUNSPECIFIED
Issue or Number:4
Classification Code:PACS: 04.25.-g, 04.25.Nx, 04.30.Db, 04.70.Bw
Record Number:CaltechAUTHORS:20130923-101026906
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:41474
Deposited By: Jason Perez
Deposited On:23 Sep 2013 19:39
Last Modified:03 Oct 2019 05:49

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