Analysis of the transverse effect of Einstein's gravitational waves

TL;DR

This paper examines the transverse effects of Einstein's gravitational waves in different gauges, clarifies the physical nature of tidal forces, and compares them with scalar-tensor gravity waves to enhance understanding of gravitational wave polarization.

Contribution

It provides a detailed analysis of the transverse effect of Einstein's GWs in various gauges and introduces a scalar-tensor gravity wave example with both transverse and longitudinal modes.

Findings

Tidal forces act orthogonally to wave propagation.

Purely transverse GWs are massless and propagate at light speed.

Scalar-tensor gravity waves can have longitudinal components.

Abstract

The investigation of the transverse effect of gravitational waves (GWs) could constitute a further tool to discriminate among several relativistic theories of gravity on the ground. After a review of the TT gauge, the transverse effect of GWs arising by standard general relativity (called Einstein's GWs in this paper) is reanalized with a different choice of coordinates. In the chosen gauge test masses have an apparent motion in the direction of propagation of the wave, while in the transverse direction they appear at rest. Of course, this is only a gauge artefact. In fact, from careful investigation of this particular gauge, it is shown that the tidal forces associated with GWs act along the directions orthogonal to the direction of propagation of waves. In the analysis it is also shown, in a heuristic way, that the transverse effect of Einstein's GWs arises from the propagation of the waves at the speed of the light, thus only massless GWs are purely transverse. But, because the physics of gravitational waves has to be investigated by studing the tidal forces as appearing in the geodesic deviation equation and directly in a laboratory environment on Earth, an analysis of these tidal forces and of the transverse effect in the frame of the local observer is also performed. After this, for a further better understanding of the transverse effect, an example of a wave, which arises from scalar tensor gravity, with both transverse and genuinely longitudinal modes is given and discussed. In the example the connection between the longitudinal component and the velocity of the wave will be mathematical shown. At the end of this paper the review of the TT gauge is completed, recovering the gauge invariance between the presented gauge and the TT one.