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

TL;DR

This paper explores the detailed motion of free test masses in gravitational waves, introducing 'electric' and 'magnetic' components of the gravitational force, and shows that the magnetic component can significantly affect interferometer responses.

Contribution

It introduces the concept of magnetic components of gravitational force in wave detection and quantifies their impact on interferometer response functions.

Findings

Magnetic component contributes up to 10% correction in response functions.

Full response function derived for arbitrary polarization.

Magnetic effects are essential for accurate data analysis.

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 wave-front 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 explicitely 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 mis-estimated.