2.2 Gravitational wave polarizations

Because of the equivalence principle, single isolated particles cannot be used to measure gravitational waves: they fall freely in any gravitational field and experience no effects from the passage of the wave. Instead, one must look for inhomogeneities in the gravitational field, which are the tidal forces carried by the waves, and which can be measured only by comparing the positions or interactions of two or more particles.

In general relativity, gravitational radiation is represented by a second rank, symmetric trace-free tensor. In a general coordinate system, and in an arbitrary gauge (coordinate choice), this tensor has ten independent components. However, as in the electromagnetic case, gravitational radiation has only two independent states of polarization in Einstein’s theory: the plus polarization and the cross polarization (the names being derived from the shape of the equivalent force fields that they produce). In contrast to electromagnetic waves, the angle between the two polarization states is π∕4 rather than π ∕2. This is illustrated in Figure 1View Image, where the response of a ring of free particles in the (x,y ) plane to plus-polarized and cross-polarized gravitational waves traveling in the z-direction is shown. The effect of the waves is to cause a tidal deformation of the circular ring into an elliptical ring with the same area. This tidal deformation caused by passing gravitational waves is the basic principle behind the construction of gravitational wave antennas.

View Image

Figure 1: In Einstein’s theory, gravitational waves have two independent polarizations. The effect on proper separations of particles in a circular ring in the (x,y)-plane due to a plus-polarized wave traveling in the z-direction is shown in (a) and due to a cross-polarized wave is shown in (b). The ring continuously gets deformed into one of the ellipses and back during the first half of a gravitational wave period and gets deformed into the other ellipse and back during the next half.

The two independent polarizations of gravitational waves are denoted h+ and h×. These are the two primary time-dependent observables of a gravitational wave. The polarization of gravitational waves from a source, such as a binary system, depends on the orientation of the dynamics inside the source relative to the observer. Therefore, measuring the polarization provides information about, for example, the orientation of the binary system.

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