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Towards adiabatic waveforms for inspiral into Kerr black holes: I. A new model of the source for the time domain perturbation equation
General Relativity and Quantum Cosmology · Submitted 5 Mar 2007
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our comparisons with earlier work show an order of magnitude gain in performance (speed) and numerical errors less than 1% for a large fraction of parameter space.
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The abstract, sentence by sentence
We revisit the problem of the emission of gravitational waves from a test mass orbiting and thus perturbing a Kerr black hole. The source term of the Teukolsky perturbation equation contains a Dirac delta function which represents a point particle. We present a technique to effectively model the delta function and its derivatives using as few as four points on a numerical grid. The source term is then incorporated into a code that evolves the Teukolsky equation in the time domain as a (2+1) dimensional PDE. The waveforms and energy fluxes are extracted far from the black hole. Our comparisons with earlier work show an order of magnitude gain in performance (speed) and numerical errors less than 1% for a large fraction of parameter space. As a first application of this code, we analyze the effect of finite extraction radius on the energy fluxes. This paper is the first in a series whose goal is to develop adiabatic waveforms describing the inspiral of a small compact body into a massive Kerr black hole.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We revisit the problem of the emission of gravitational waves from a test mass orbiting and thus perturbing a Kerr black hole. | background 0.98 | 0.31 | 0.03 | unclear 0.50 |
| s1 | The source term of the Teukolsky perturbation equation contains a Dirac delta function which represents a point particle. | background 0.99 | 0.09 | 0.03 | asserted 1.00 |
| s2 | We present a technique to effectively model the delta function and its derivatives using as few as four points on a numerical grid. | method 0.86 | 0.95 | 0.13 | asserted 0.97 |
| s3 | The source term is then incorporated into a code that evolves the Teukolsky equation in the time domain as a (2+1) dimensional PDE. | method 0.99 | 0.93 | 0.05 | asserted 1.00 |
| s4 | The waveforms and energy fluxes are extracted far from the black hole. | method 0.98 | 0.91 | 0.05 | asserted 0.99 |
| s5 | Our comparisons with earlier work show an order of magnitude gain in performance (speed) and numerical errors less than 1% for a large fraction of parameter space. | result 1.00 | 0.94 | 0.41 | asserted 1.00 |
| s6 | As a first application of this code, we analyze the effect of finite extraction radius on the energy fluxes. | contribution 0.92 | 0.94 | 0.05 | asserted 0.88 |
| s7 | This paper is the first in a series whose goal is to develop adiabatic waveforms describing the inspiral of a small compact body into a massive Kerr black hole. | future work 0.98 | 0.41 | 0.10 | asserted 1.00 |
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The paper
Original abstract
We revisit the problem of the emission of gravitational waves from a test mass orbiting and thus perturbing a Kerr black hole. The source term of the Teukolsky perturbation equation contains a Dirac delta function which represents a point particle. We present a technique to effectively model the delta function and its derivatives using as few as four points on a numerical grid. The source term is then incorporated into a code that evolves the Teukolsky equation in the time domain as a (2+1) dimensional PDE. The waveforms and energy fluxes are extracted far from the black hole. Our comparisons with earlier work show an order of magnitude gain in performance (speed) and numerical errors less than 1% for a large fraction of parameter space. As a first application of this code, we analyze the effect of finite extraction radius on the energy fluxes. This paper is the first in a series whose goal is to develop adiabatic waveforms describing the inspiral of a small compact body into a massive Kerr black hole.
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References
How later papers used it
48 later papers cite it
2 papers by the same authors are listed below: 2 used its method or tool.
Uses its method or tool 2 of 26 papers with this label · 2 by the same authors
By the same authors
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Obtained its numerical fluxes through the time-domain Teukolsky code of this paper.
Testing eccentric corrections to the radiation-reaction force in the test-mass limit of effective-one-body models (2024) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
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Produced its waveforms by computing inspiral and plunge worldlines following the procedure described in this paper.
Learning about black hole binaries from their ringdown spectra (2019) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
How the literature uses it
45 arXiv papers cite this in 84 sentences
Papers citing it · 35 sentences without a confident label
Uses its method or tool 23 papers
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In this paper, we combine EOB with the time-domain Teukolsky code developed in Refs. [ref] to extend the ideas of Refs. [ref] in several directions.
Modeling multipolar gravitational-wave emission from small mass-ratio mergers · Introduction · 0.91
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The analysis is performed by comparing the analytical fluxes, computed from the eccentric RR force in the TM limit, against numerical fluxes that are computed by solving the Teukolsky equation [ref] through the use of a frequency-domain (FD) [ref] and a time-domain (TD) [ref] code.
Testing eccentric corrections to the radiation-reaction force in the test-mass limit of effective-one-body models · Introduction · 0.95
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We then generate the ppBHPT waveform for this mass ratio using the framework developed in Refs. [ref] .
On the approximate relation between black-hole perturbation theory and numerical relativity · Scaling between NR and perturbation theory · 1.00
Compares with it 1 paper
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Our phase-space formulation differs in two ways from previous approaches to modelling the merger-ringdown at leading order within GSF theory [ref] : first, our approach maintains the rapid waveform generation framework of the inspiral; second, it can be systematically applied beyond leading order.
Self-force framework for merger-ringdown waveforms · Introduction · 0.98
Cites it as background 12 papers
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On the other hand, the BHPT framework linearizes the Einstein equation, treating smaller black hole to be a point particle [ref] .
Mapping between black-hole perturbation theory and numerical relativity II: gravitational-wave momentum · Introduction · 0.95
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In contrast, adiabatic point particle black hole perturbation theory (ppBHPT) [ref] offers a reliable modeling approach for extreme mass ratio inspirals (EMRI) ($q →∞$) (Fig. [ref]).
On the approximate relation between black-hole perturbation theory and numerical relativity · Introduction · 0.82
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After decades of progress [ref] , adiabatic waveforms for generic Kerr orbits were obtained in 2021 [ref] .
Adiabatic waveforms from extreme-mass-ratio inspirals: an analytical approach · Introduction · 0.97
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