# 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:

- 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}

}