Detecting the beaming effect of gravitational waves

The models currently used in the detection of gravitational waves (GWs) either do not consider a relative motion between the center of mass of the source and the observer or usually only consider its effect on the frequencies of GWs. However, it is known for light waves that a relative motion not only changes the frequencies but also the brightness of the source, the latter of which is called the "beaming effect." We investigate such an effect for GWs and find that the observed amplitude of a GW signal, unlike the behavior of light, is not a monotonic function of the relative velocity and responds differently to the two GW polarizations. We attribute the difference to a rotation of the wave vector, as well as a reorientation of the GW polarizations. We find that even for velocities as small as 0.25% of the speed of light, ignoring the aforementioned beaming effect could induce a systematic error that is larger than the designated calibration accuracy of LIGO. This error could lead to an incorrect estimation of the distance and orbital inclination of a GW source, or result in a spurious signal that appears to be incompatible with general relativity.