Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perturbative extraction of gravitational waveforms generated with
  Numerical Relativity   We derive an analytical expression for extracting the gravitational waveforms
at null infinity using the Weyl scalar $\psi_4$ measured at a finite radius.
Our expression is based on a series solution in orders of 1/r to the equations
for gravitational perturbations about a spinning black hole. We compute this
expression to order $1/r^2$ and include the spin parameter $a$ of the Kerr
background. We test the accuracy of this extraction procedure by measuring the
waveform for a merging black-hole binary at ten different extraction radii (in
the range r/M=75-190) and for three different resolutions in the convergence
regime. We find that the extraction formula provides a set of values for the
radiated energy and momenta that at finite extraction radii converges towards
the expected values with increasing resolution, which is not the case for the
`raw' waveform at finite radius. We also examine the phase and amplitude errors
in the waveform as a function of observer location and again observe the
benefits of using our extraction formula. The leading corrections to the phase
are ${\cal O}(1/r)$ and to the amplitude are ${\cal O}(1/r^2)$. This method
provides a simple and practical way of estimating the waveform at infinity, and
may be especially useful for scenarios such as well separated binaries, where
the radiation zone is far from the sources, that would otherwise require
extended simulation grids in order to extrapolate the `raw' waveform to
infinity. Thus this method saves important computational resources and provides
an estimate of errors.

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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: math
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph