Components of the gravitational force in the field of a gravitational wave

Abstract

Gravitational waves bring about the relative motion of free test masses. The detailed knowledge of this motion is important conceptually and practically, because the mirrors of laser interferometric detectors of gravitational waves are essentially free test masses. There exists an analogy between the motion of free masses in the field of a gravitational wave and the motion of free charges in the field of an electromagnetic wave. In particular, a gravitational wave drives the masses in the plane of the wavefront and also, to a smaller extent, back and forth in the direction of the wave's propagation. To describe this motion, we introduce the notion of ‘electric’ and ‘magnetic’ components of the gravitational force. This analogy is not perfect, but it reflects some important features of the phenomenon. Using different methods, we demonstrate the presence and importance of what we call the ‘magnetic’ component of motion of free masses. It contributes to the variation of distance between a pair of particles. We explicitly derive the full response function of a 2-arm laser interferometer to a gravitational wave of arbitrary polarization. We give a convenient description of the response function in terms of the spin-weighted spherical harmonics. We show that the previously ignored ‘magnetic’ component may provide a correction of up to 10%, or so, to the usual ‘electric’ component of the response function. The ‘magnetic’ contribution must be taken into account in the data analysis, if the parameters of the radiating system are not to be misestimated.