### 6.2 Polarization of gravitational waves

As noted in Section 2, in Einstein’s theory gravitational waves have two independent polarizations, usually denoted and  [262]. A general wave will be a linear combination of both. Rotating sources typically emit both polarizations with a phase delay between them, leading to elliptical polarization patterns. Depending on the nature of the source such polarizations can be detected either with a single detector (in the case of continuous wave sources) or with a network of detectors (in the case of burst sources).

While Einstein’s general relativity predicts only two independent polarizations, there are other theories of gravitation in which there are additional states of polarization. For instance, in Fierze–Jordan–Brans–Dicke theory [394] there are four polarization degrees of freedom more than in Einstein’s theory. Therefore, an unambiguous determination of the polarization of the waves will be of fundamental importance.

In the case of a burst source, to determine two polarization states, source direction and amplitude requires three detectors, observing other polarizations would require the use of more than three detectors (see, for example, Will [394]). The scalar polarization mode of Brans–Dicke, for example, expands a transverse ring of test particles without changing its shape. This is the breathing mode, or monopole polarization. If such a wave is incident from above on an interferometer, it will not register at all. But if it comes in along one of the arms, then, since it acts transversely, it will affect only the other arm and leave a signal. If the wave is seen with enough detectors, then it is possible to determine that it has scalar polarization. Note that a measurement such as this can make a qualitative change in physics: a single measurement could put general relativity in jeopardy.

Polarization measurements have an important application in astronomy. The polarization of the waves contains orientation information. For example, a binary system emits purely circular polarization along the angular momentum axis, but purely linear polarization in its equatorial plane. By measuring the polarization of waves from a binary (or from a spinning neutron star) one can determine the orientation and inclination of its spin axis. This is a piece of information that is usually very hard to extract from optical observations. We will return to this discussion in Section 7.1.1.