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Quasi normal modes: A simple derivation of the level spacing of the frequencies
General Relativity and Quantum Cosmology · Submitted 5 Oct 2003
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The analysis shows that the result is closely linked to the thermal nature of horizons and arises from the exponential redshift of the wave modes close to the horizon.
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The abstract, sentence by sentence
It is known that the imaginary parts of the frequencies of the quasi normal modes of the Schwarzschild black hole are equally spaced, with the level spacing dependent only on the surface gravity. We generalize this result to a wider class of spacetimes and provide a simple derivation of the imaginary parts of the frequencies. The analysis shows that the result is closely linked to the thermal nature of horizons and arises from the exponential redshift of the wave modes close to the horizon.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | It is known that the imaginary parts of the frequencies of the quasi normal modes of the Schwarzschild black hole are equally spaced, with the level spacing dependent only on the surface gravity. | background 1.00 | 0.04 | 0.10 | asserted 1.00 |
| s1 | We generalize this result to a wider class of spacetimes and provide a simple derivation of the imaginary parts of the frequencies. | contribution 1.00 | 0.95 | 0.27 | asserted 0.99 |
| s2 | The analysis shows that the result is closely linked to the thermal nature of horizons and arises from the exponential redshift of the wave modes close to the horizon. | interpretation 0.98 | 0.89 | 0.44 | asserted 1.00 |
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The paper
Original abstract
It is known that the imaginary parts of the frequencies of the quasi normal modes of the Schwarzschild black hole are equally spaced, with the level spacing dependent only on the surface gravity. We generalize this result to a wider class of spacetimes and provide a simple derivation of the imaginary parts of the frequencies. The analysis shows that the result is closely linked to the thermal nature of horizons and arises from the exponential redshift of the wave modes close to the horizon.
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References
How the literature uses it
12 arXiv papers cite this in 17 sentences
Papers citing it · 4 sentences without a confident label
Uses its method or tool 2 papers
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In order to obtain the QNM of the CDBH, we applied an approximation method given in Refs. [ref] to the Zerilli equation (20).
Quasinormal modes of charged dilaton black holes and their entropy spectra · Conclusion · 1.00
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Gaining inspiration from the studies [ref] , here we use an approximation method in order to define the QNMs.
Spectroscopy of Rindler Modified Schwarzschild Black Hole · QNMs and entropy/area spectra of GBH · 0.93
Compares with it 2 papers
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For large values of $n$, this formula greatly resembles the behaviour of frequency overtones of Schwarzschild black hole perturbations in General Relativity, which follows the law [ref]
Hidden conformal symmetries for black holes in modified gravity · Some consequences of the conformal symmetries · 0.97
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This can be compared with the celebrated simple derivation from the poles of the scattering amplitude in the Born approximation [ref] .
Love symmetry · Future directions · 1.00
Cites it as support 1 paper
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For Schwarzschild black holes, and more generally single-horizon black holes, it has been demonstrated that: * WKB inspired approximations [ref] ; * phase-amplitude methods [ref] ; * continued fraction approximations for the QNFs [ref] ; * monodromy techniques [ref] ; * Born approximations [ref] ; all agree on this general $ω_n = (offset) + i n (gap)$ form for the QNFs with the surface gravity $κ↔1/b$ governing the “gap” between the high-lying modes.
Semi-analytic results for quasi-normal frequencies · Black hole QNFs · 0.97
Cites it as background 6 papers
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The third possibility is the $SL(2)$ algebra,[There have been previous attempts to interpret the modes [ref] geometrically [ref] , many of which attempted to construct an $SL(2,ℝ)$ symmetry near the horizon of non-extremal black holes.
pp-Waves and the Hidden Symmetries of Black Hole Quasinormal Modes · Introduction · 0.90
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Most of the work on quasinormal modes of rotating non-extremal black holes involves numerical methods [ref] , though there are a few analytic methods for the Schwarzschild solution (e.g., [ref] ) and the (near-) extremal Kerr black hole (e.g., see [ref] and references within).
Black Hole Scattering from Monodromy · Future Directions · 0.96
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We are particularly interested in understanding the [equation] behaviour that has been encountered in very many different analyses, often in the context of black hole physics, but by no means limited to black hole physics [ref] .
Highly-damped quasi-normal frequencies for piecewise Eckart potentials · Introduction · 0.85
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