In the preceding subsections, we discussed the propagation and detection of gravitational waves. It is perhaps useful now to say a few words about the production of gravitational waves before diving into the particular sources of interest for this article, binary neutron star systems.

We have discussed solutions to the homogeneous (Tap = 0) version of (1), which describe the propagation of GWs in the far wave zone. The generation of gravitational waves requires a source, and is therefore described by (1) with Tap=0. In fact, to lowest order, the relevant property of the source is the mass density of the source, p(t, x), or more specifically, the mass quadrupole moments.

The relevant quadrupole moments depend on the direction from the source at which the gravitational wave is detected. In the limit of a negligibly gravitating source, the moments are given by the integrals

Here, x = {x, y, z} are Cartesian coordinates centered on the source with the z-axis being defined by the direction to the detector and t is time. In terms of these integrals, the relevant components of the solution to (1) with source is

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