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Falloff of the Weyl scalars in binary black hole spacetimes
General Relativity and Quantum Cosmology · Submitted 4 May 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In contrast with previous results, we observe that all the Weyl scalars fall off according to the predictions of the theorem.
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
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The abstract, sentence by sentence
The peeling theorem of general relativity predicts that the Weyl curvature scalars Psi_n (n=0...4), when constructed from a suitable null tetrad in an asymptotically flat spacetime, fall off asymptotically as r^(n-5) along outgoing radial null geodesics. This leads to the interpretation of Psi_4 as outgoing gravitational radiation at large distances from the source. We have performed numerical simulations in full general relativity of a binary black hole inspiral and merger, and have computed the Weyl scalars in the standard tetrad used in numerical relativity. In contrast with previous results, we observe that all the Weyl scalars fall off according to the predictions of the theorem.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The peeling theorem of general relativity predicts that the Weyl curvature scalars Psi_n (n=0...4), when constructed from a suitable null tetrad in an asymptotically flat spacetime, fall off asymptotically as r^(n-5) along outgoing radial null geodesics. | background 1.00 | 0.03 | 0.07 | asserted 0.99 |
| s1 | This leads to the interpretation of Psi_4 as outgoing gravitational radiation at large distances from the source. | background 0.65 | 0.05 | 0.04 | asserted 0.96 |
| s2 | We have performed numerical simulations in full general relativity of a binary black hole inspiral and merger, and have computed the Weyl scalars in the standard tetrad used in numerical relativity. | method 0.75 | 0.97 | 0.04 | asserted 1.00 |
| s3 | In contrast with previous results, we observe that all the Weyl scalars fall off according to the predictions of the theorem. | result 1.00 | 0.96 | 0.89 | asserted 1.00 |
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The paper
Original abstract
The peeling theorem of general relativity predicts that the Weyl curvature scalars Psi_n (n=0...4), when constructed from a suitable null tetrad in an asymptotically flat spacetime, fall off asymptotically as r^(n-5) along outgoing radial null geodesics. This leads to the interpretation of Psi_4 as outgoing gravitational radiation at large distances from the source. We have performed numerical simulations in full general relativity of a binary black hole inspiral and merger, and have computed the Weyl scalars in the standard tetrad used in numerical relativity. In contrast with previous results, we observe that all the Weyl scalars fall off according to the predictions of the theorem.
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References
How the literature uses it
6 arXiv papers cite this in 7 sentences
Papers citing it · 4 sentences without a confident label
Compares with it 1 paper
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OML warmly thanks the Max Planck Institute - Albert Einstein Institute for great hospitality during the final stages of this work and Cecilia Chirenti for remarking the possibility to use [ref] for a comparison with modified theories of gravity.
Non-analytical power law correction to the Einstein-Hilbert action: gravitational wave propagation · Concluding remarks · 0.98
Cites it as background 2 papers
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This is known as the peeling property; see [ref] for discussions of various aspects of peeling.
Mode stability on the real axis · Waves with no incoming radiation · 0.99
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The behaviour of Weyl scalars in GR in the case of a binary black hole inspiral and merger has recently been numerically investigated in [ref] .
Non-analytical power law correction to the Einstein-Hilbert action: gravitational wave propagation · Minkowskian limit · 0.98
What it cites · 9 sentences without a confident label
Builds on 1 paper
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In this work, we follow up the study carried out in [ref] , where the radial falloff of the Weyl scalars was measured in a BBH spacetime and compared with the results expected from the peeling theorem.
The Asymptotic Falloff of Local Waveform Measurements in Numerical Relativity · Introduction · 0.82
Uses the method or tool of 8 papers
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Our numerical BBH solutions were obtained using the Llama code [ref] to solve Einstein's equations in the BSSN [ref] formalism with the moving puncture method [ref] using eighth-order finite differencing.
On the Numerical Integration of Einstein's Field Equations · Numerical implementation · 1.00
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Our numerical BBH solutions were obtained using the Llama code [ref] to solve Einstein's equations in the BSSN [ref] formalism with the moving puncture method [ref] using eighth-order finite differencing.
High accuracy binary black hole simulations with an extended wave zone · Numerical implementation · 1.00
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Our numerical BBH solutions were obtained using the Llama code [ref] to solve Einstein's equations in the BSSN [ref] formalism with the moving puncture method [ref] using eighth-order finite differencing.
Gravitational wave extraction from an inspiraling configuration of merging black holes · Numerical implementation · 1.00
Compares with 1 paper
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Table [ref] shows the falloff rates for each scalar along $λ_1$ as well as the rate quoted in [ref] and the rate expected from the peeling theorem.
The Asymptotic Falloff of Local Waveform Measurements in Numerical Relativity · Results · 0.93
Cites as background 28 papers
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The asymptotic properties (such as the radial falloff of the Weyl scalars) of binary-black-hole (BBH) spacetimes have been investigated [ref] , and the algebraic character of BBH spacetimes has been studied [ref] .
Degeneracy measures for the algebraic classification of numerical spacetimes · Introduction · 1.00
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The asymptotic properties (such as the radial falloff of the Weyl scalars) of binary-black-hole (BBH) spacetimes have been investigated [ref] , and the algebraic character of BBH spacetimes has been studied [ref] .
Algebraic Classification of Numerical Spacetimes and Black-Hole-Binary Remnants · Introduction · 1.00
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The asymptotic properties (such as the radial falloff of the Weyl scalars) of binary-black-hole (BBH) spacetimes have been investigated [ref] , and the algebraic character of BBH spacetimes has been studied [ref] .
The Asymptotic Falloff of Local Waveform Measurements in Numerical Relativity · Introduction · 1.00
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