Branching of quasinormal modes for nearly extremal Kerr black holes

2012/12/13 by Huan Yang, Fan Zhang, Aaron Zimmerman +3 · 7 citations
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Condensed matter physics #Cosmology and Gravitation Theories #Eikonal equation #Gravitational wave #Mathematical physics #Merge (version control) #Physics #Quantum mechanics #Quasinormal mode #Spacetime #Spins #gr-qc #hep-th

paper · pdf · doi:10.1103/physrevd.87.041502

published as Phys. Rev. D 87, 041502(R) (2013) · 5 pages, 3 figures

arxiv created 2012/12/13 · openalex publication_date 2013/02/22 · arxiv updated 2013/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We show that nearly extremal Kerr black holes have two distinct sets of quasinormal modes, which we call zero-damping modes (ZDMs) and damped modes (DMs). The ZDMs exist for all harmonic indices l and m\ensuremath≥0, and their frequencies cluster onto the real axis in the extremal limit. The DMs have nonzero damping for all black hole spins; they exist for all counterrotating modes (m<0) and for corotating modes with 0\ensuremath≤\ensuremathμ\ensuremath\lesssim\ensuremathμ_c=0.74 (in the eikonal limit), where \ensuremathμ\ensuremath≡m/(l+1/2). When the two families coexist, ZDMs and DMs merge to form a single set of quasinormal modes as the black hole spin decreases. Using the effective potential for perturbations of the Kerr spacetime, we give intuitive explanations for the absence of DMs in certain areas of the spectrum and for the branching of the spectrum into ZDMs and DMs at large spins.

Citations

• Unstable fields in Kerr spacetimes
• Quasinormal modes of black holes and black branes
• Perturbations of a rotating black hole. III - Interaction of the hole with gravitational and electromagnetic radiation
• Kerr-CFT and gravitational perturbations
• Microscopic Origin of the Bekenstein-Hawking Entropy
• Gravitational instabilities of superspinars
• Slow relaxation of rapidly rotating black holes

Cited by

• A massive charged scalar field in the Kerr-Newman background I: quasinormal modes, late-time tails and stability
• Quasinormal modes of nearly extremal Kerr spacetimes: spectrum bifurcation and power-law ringdown
• Towards an understanding of the force-free magnetosphere of rapidly spinning black holes
• Asymptotics of Linear Waves and Resonances with Applications to Black Holes
• Transient instability of rapidly rotating black holes
• Modes of the Kerr geometry with purely imaginary frequencies
• Small mass plunging into a Kerr black hole: Anatomy of the inspiral-merger-ringdown waveforms

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• Mode stability and shallow quasinormal modes of Kerr-de Sitter black holes away from extremality