Abstract
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.
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