A detailed study of quasinormal frequencies of the Kerr black hole

Hisashi Onozawa (Tokyo Inst. of Tech.)

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A detailed study of quasinormal frequencies of the Kerr black hole

General Relativity and Quantum Cosmology · Submitted 22 Oct 1996

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The authors' main claim We also calculate the algebraically special frequency first identified by Chandrasekhar and confirm that it coincide with the $n=8$ quasinormal frequency only at the Schwarzschild limit.

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arXiv IDgr-qc/9610048 (version 1)

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CitationHisashi Onozawa (Tokyo Inst. of Tech.). "A detailed study of quasinormal frequencies of the Kerr black hole." arXiv:gr-qc/9610048 (1996). https://pith.science/paper/R7SLNMGE

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We compute the quasinormal frequencies of the Kerr black hole using a continued fraction method. The continued fraction method first proposed by Leaver is still the only known method stable and accurate for the numerical determination of the Kerr quasinormal frequencies. We numerically obtain not only the slowly but also the rapidly damped quasinormal frequencies and analyze the peculiar behavior of these frequencies at the Kerr limit. We also calculate the algebraically special frequency first identified by Chandrasekhar and confirm that it coincide with the $n=8$ quasinormal frequency only at the Schwarzschild limit.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We compute the quasinormal frequencies of the Kerr black hole using a continued fraction method.	method 0.51	0.97	0.11	asserted 1.00
s1	The continued fraction method first proposed by Leaver is still the only known method stable and accurate for the numerical determination of the Kerr quasinormal frequencies.	background 0.94	0.06	0.08	asserted 1.00
s2	We numerically obtain not only the slowly but also the rapidly damped quasinormal frequencies and analyze the peculiar behavior of these frequencies at the Kerr limit.	contribution 0.58	0.97	0.21	asserted 1.00
s3	We also calculate the algebraically special frequency first identified by Chandrasekhar and confirm that it coincide with the $n=8$ quasinormal frequency only at the Schwarzschild limit.	result 0.97	0.89	0.20	asserted 1.00

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Original abstract

We compute the quasinormal frequencies of the Kerr black hole using a continued fraction method. The continued fraction method first proposed by Leaver is still the only known method stable and accurate for the numerical determination of the Kerr quasinormal frequencies. We numerically obtain not only the slowly but also the rapidly damped quasinormal frequencies and analyze the peculiar behavior of these frequencies at the Kerr limit. We also calculate the algebraically special frequency first identified by Chandrasekhar and confirm that it coincide with the $n=8$ quasinormal frequency only at the Schwarzschild limit.

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Cited by 12 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Amplified EFT corrections near exceptional QNMs
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EFT corrections to black hole QNM frequencies are amplified near exceptional points, with a square-root splitting that can be computed without solving the full UV theory.
Excitation factors and exceptional points of Kerr-de Sitter quasinormal modes
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The paper systematically computes quasinormal mode excitation factors for Kerr-de Sitter black holes and identifies exceptional points where overtone frequencies coincide.
Pole Skipping, Avoided Crossing, and Resonant Excitation in Kerr Quasinormal Modes near Algebraically Special Frequencies
gr-qc 2026-05 unverdicted novelty 7.0 of 10

Kerr QNM anomalies near algebraically special frequencies arise from avoided crossings with resonant excitation and pole skipping due to quasinormal-Matsubara pole-zero cancellations.
Exceptional Points and Resonance in Black Hole Ringdown
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An exceptional-point framework for black-hole ringdown characterizes resonances near avoided crossings, demonstrates enhanced mode contributions in the time domain, and identifies the EP frequency as the physically re...
Resonance of black hole quasinormal modes in coupled systems
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A new basis-invariant excitation factor for coupled black hole perturbation systems shows resonant amplification at avoided crossings between fundamental modes of different fields in the Einstein-Maxwell-axion theory.

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Test-Field vs Physical Quasi-Normal Modes in Scalar-Tensor Theories
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Test-field QNM spectra of BCL black holes deviate strongly from physical axial gravitational QNM spectra at high overtones, while fundamental modes remain close.
Linear mode stability of Kerr-Newman and its quasinormal modes
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Kerr-Newman black holes are numerically shown to be linearly stable against all gravito-electromagnetic perturbations up to 99.999% of extremality, and their quasinormal-mode spectrum is mapped across the full three-p...
Exceptional Points in Scalar Quasinormal Modes of Rastall String-Fluid Black Holes
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A two-parameter search in a Rastall-string-fluid black hole reveals a defective spectral degeneracy (exceptional point) with converging eigenvector coalescence and Jordan response.
Extended parameterized spin expansion formalism for ringdown analysis with GW250114
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Two-scalar-field $f(R)$ Thick Branes, Gravitational Resonances and Quasinormal Modes
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In ghost-free two-scalar f(R) thick branes, internal structure produces no narrow real-axis tensor resonances; quasinormal modes are broad with quality factors 0.9-1.9.
Extreme Gravity Tests with Gravitational Waves from Compact Binary Coalescences: (II) Ringdown
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Black hole spectroscopy, extracting multiple quasinormal modes from ringdown signals, can test Kerr dynamics, but needs ringdown signal-to-noise ratios near 100, reachable only with third-generation and space-based detectors.
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How the literature uses it

29 arXiv papers cite this in 37 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 24 sentences without a confident label

Builds on it 1 paper

Then, in Sec. [ref], we search for QNM frequencies $ω_QNM$ recovering previous results [ref] , while extending most of them to higher BH rotation.

Quasinormal modes and excitation factors of Kerr black holes · Results · 0.90

Uses its method or tool 2 papers

Leaver's approach, often referred to as the Continued Fraction method, allows for a high-accuracy computation of QNMs on a large part of the complex spectrum [ref] .

Test-Field vs Physical Quasi-Normal Modes in Scalar-Tensor Theories · Introduction · 0.93
An independent verification of the overtones can be obtained by Taylor-expanding the metric function in a compact radial coordinate, casting the wave equation into a form with rational coefficients, and applying Leaver's continued-fraction method [ref] , which was used in a great number of studies for finding precise quasinormal modes [ref] .

Gravitational perturbations of a regular T-duality inspired black hole: Quasinormal modes, excitation factors, and time-domain evolution · Conclusions · 0.92

Compares with it 1 paper

Similar branching behavior has been found in Kerr and Kerr-Newman BHs [ref] .

Dynamical behavior of the $C$-metric: charged scalar fields, quasinormal modes and superradiance · Quasinormal modes of charged scalar fields · 0.97

Cites it as support 1 paper

Since $D_+(-a)=-D_-(a)$, the angular velocities and Lyapunov exponents possess the mirror symmetry under the transformation of $a→-a$, [equation] This symmetry implies [ref] that the QNFs for corotating and counterrotating orbits are not independent.

Phase diagrams of quasinormal frequencies for Schwarzschild, Kerr, and Taub-NUT black holes · Kerr black holes · 0.98

Cites it as background 8 papers

In General Relativity in vacuum, that is, in the case of Kerr BHs [ref] , it has long been known that certain overtones exhibit a peculiar behavior in the complex plane [ref] .

Resonance of black hole quasinormal modes in coupled systems · Introduction · 0.95
After Detweiler, several investigators studied ZDMs of near-extremal black holes, both analytically and numerically [ref] .

Synchronous frequencies of extremal Kerr black holes: resonances, scattering and stability · Introduction · 0.92
In general relativity (GR), the remnant is expected to relax to a Kerr black hole, whose QNM frequencies and damping times are uniquely determined by the remnant mass and spin [ref] .

Extended parameterized spin expansion formalism for ringdown analysis with GW250114 · Introduction · 0.92

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