Deviation of geodesics and particle trajectories in a gravitational wave of the Bianchi type VI universe

TL;DR

This paper derives exact solutions for geodesic deviation in a Bianchi type VI universe under a strong primordial gravitational wave, providing insights into tidal accelerations and coordinate transformations relevant in relativity.

Contribution

It presents new exact solutions for geodesic deviation and tidal accelerations in a Bianchi type VI universe with gravitational waves, including explicit coordinate transformations and metric forms.

Findings

Exact solutions for geodesic deviation in Bianchi type VI universe

Explicit form of tidal acceleration vector in gravitational waves

Coordinate transformation and metric form for primordial gravitational waves

Abstract

For the Bianchi type VI universe, exact solutions of the equation of geodesic deviation in a strong primordial gravitational wave in a privileged coordinate system are obtained. The solutions refer to Shapovalov's gravitational-wave models of spacetime and allow the existence of complete integrals of the Hamilton-Jacobi equation for test particles. For all the solutions obtained, the analytical form of the tidal acceleration vector in a strong primordial gravitational wave is obtained. An explicit form of the coordinate transformation, an explicit form of the metric of the primordial gravitational wave of the Bianchi type VI universe, and the form of the tidal acceleration vector in the laboratory synchronous coordinate system are obtained. The synchronous coordinate system is associated with a freely falling observer and allows the observer to separate time and spatial coordinates, as well as to synchronize time at different points in space. The presented mathematical approach can be applied both in the general theory of relativity and in modified theories of gravity.