Breaking of parallelograms in presence of torsion: an equivalent alternative approach to detect gravitational waves

The equations for gravitational plane waves produced by a typical binary system as a solution of linear approximation of Einstein equations are derived. The dynamics of the corresponding gravitational field is analyzed in a four-dimensional space-time manifold, endowed with a metric and taking into account torsion. In this context, the geometrical reason of the existence of torsion due to the presence of gravitational waves (GW) is highlighted and the geodesic deviation is obtained taking into account both curvature and torsion. In a laser interferometer gravitational detector, the delay time between the arrivals of the two laser beams traveling back and forth along the two arms in presence of gravitational waves is interpreted from this point of view. This delay is calculated for the NS–NS binary pulsar (1913 + 16) in two specific orientations with respect to the experimental device, corresponding to different polarizations of gravitational waves. In the specific case of this example, it is shown that the results obtained in the context of the standard general relativity (GR) and in the framework of teleparallel gravity are equivalent.