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Title: Towards a wave-extraction method for numerical relativity. V. Estimating the gravitational-wave content of spatial hypersurfaces

Abstract

We extract the Weyl scalars in the quasi-Kinnersley tetrad by finding initially the (gauge-, tetrad-, and background-independent) transverse quasi-Kinnersley frame. This step still leaves two undetermined degrees of freedom: the ratio |{psi}{sub 0}|/|{psi}{sub 4}|, and one of the phases (the product |{psi}{sub 0}|{center_dot}|{psi}{sub 4}| and the sum of the phases are determined by the so-called Beetle-Burko radiation scalar). The residual symmetry ('spin/boost') can be removed by gauge fixing of spin coefficients in two steps: First, we break the boost symmetry by requiring that {rho} corresponds to a global constant mass parameter that equals the ADM mass (or, equivalently in perturbation theory, that {rho} or {mu} equal their values in the no-radiation limits), thus determining the two moduli of the Weyl scalars |{psi}{sub 0}|, |{psi}{sub 4}|, while leaving their phases as yet undetermined. Second, we break the spin symmetry by requiring that the ratio {pi}/{tau} gives the expected polarization state for the gravitational waves, thus determining the phases. Our method of gauge fixing--specifically its second step--is appropriate for cases for which the Weyl curvature is purely electric. Applying this method to Misner and Brill-Lindquist data, we explicitly find the Weyl scalars {psi}{sub 0} and {psi}{sub 4} in the quasi-Kinnersley tetrad.

Authors:
 [1]
  1. Department of Physics, University of Alabama in Huntsville, Huntsville, Alabama 35899 (United States)
Publication Date:
OSTI Identifier:
21020408
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.75.084039; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COSMOLOGY; DEGREES OF FREEDOM; GRAVITATIONAL WAVES; MASS; PERTURBATION THEORY; POLARIZATION; SCALARS; SPIN; SYMMETRY; WEYL UNIFIED THEORY

Citation Formats

Burko, Lior M. Towards a wave-extraction method for numerical relativity. V. Estimating the gravitational-wave content of spatial hypersurfaces. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.084039.
Burko, Lior M. Towards a wave-extraction method for numerical relativity. V. Estimating the gravitational-wave content of spatial hypersurfaces. United States. doi:10.1103/PHYSREVD.75.084039.
Burko, Lior M. Sun . "Towards a wave-extraction method for numerical relativity. V. Estimating the gravitational-wave content of spatial hypersurfaces". United States. doi:10.1103/PHYSREVD.75.084039.
@article{osti_21020408,
title = {Towards a wave-extraction method for numerical relativity. V. Estimating the gravitational-wave content of spatial hypersurfaces},
author = {Burko, Lior M.},
abstractNote = {We extract the Weyl scalars in the quasi-Kinnersley tetrad by finding initially the (gauge-, tetrad-, and background-independent) transverse quasi-Kinnersley frame. This step still leaves two undetermined degrees of freedom: the ratio |{psi}{sub 0}|/|{psi}{sub 4}|, and one of the phases (the product |{psi}{sub 0}|{center_dot}|{psi}{sub 4}| and the sum of the phases are determined by the so-called Beetle-Burko radiation scalar). The residual symmetry ('spin/boost') can be removed by gauge fixing of spin coefficients in two steps: First, we break the boost symmetry by requiring that {rho} corresponds to a global constant mass parameter that equals the ADM mass (or, equivalently in perturbation theory, that {rho} or {mu} equal their values in the no-radiation limits), thus determining the two moduli of the Weyl scalars |{psi}{sub 0}|, |{psi}{sub 4}|, while leaving their phases as yet undetermined. Second, we break the spin symmetry by requiring that the ratio {pi}/{tau} gives the expected polarization state for the gravitational waves, thus determining the phases. Our method of gauge fixing--specifically its second step--is appropriate for cases for which the Weyl curvature is purely electric. Applying this method to Misner and Brill-Lindquist data, we explicitly find the Weyl scalars {psi}{sub 0} and {psi}{sub 4} in the quasi-Kinnersley tetrad.},
doi = {10.1103/PHYSREVD.75.084039},
journal = {Physical Review. D, Particles Fields},
number = 8,
volume = 75,
place = {United States},
year = {Sun Apr 15 00:00:00 EDT 2007},
month = {Sun Apr 15 00:00:00 EDT 2007}
}
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