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The transverse traceless gauge and quadrupole sources

American Journal of Physics -- October 2008 -- Volume 76, Issue 10, pp. 930-933

Issue Date: October 2008
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ISSN:
0002-9505 (print)  
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Richard H. Price
Center for Gravitational Wave Astronomy and Department of Physics and Astronomy, University of Texas at Brownsville, Brownsville, Texas 78520

Yan Wang
Center for Gravitational Wave Astronomy and Department of Physics and Astronomy, University of Texas at Brownsville, Brownsville, Texas 78520 and Department of Astronomy, Nanjing University, Nanjing 210093, China
A gravitational wave propagating in the +z direction is usually described by the transverse spatial components hxx, hyy, hxy in the transverse traceless gauge in which hxx+hyy=0. The transverse components are not changed by a gauge transformation, which implies that the traceless condition must be automatically met. We analyze how this comes about in the calculation of the waves in an explicit example, a circular binary orbit of equal mass points. This calculation is a useful exercise in linearized general relativity and gravitational waves, and a model of an important astrophysical source of detectable waves. We also demonstrate automatic transverse tracelessness for the general case of a slow motion source.

©2008 American Association of Physics Teachers
History: Received 6 December 2007; accepted 9 May 2008
Permalink: http://dx.doi.org/10.1119/1.2937908

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