Gravitational wave of the Bianchi VII universe: particle trajectories, geodesic deviation and tidal accelerations

TL;DR

This paper derives exact solutions for particle trajectories, geodesic deviation, and tidal accelerations in a Bianchi VII universe gravitational wave model, providing tools for studying primordial gravitational waves and their effects.

Contribution

It presents the first exact solutions for geodesic deviation and tidal accelerations in a Bianchi VII universe gravitational wave model, including transformations to a synchronous reference system.

Findings

Explicit form of the gravitational wave metric in a synchronous system

Exact solutions for geodesic deviation and tidal accelerations

Application to primordial gravitational wave analysis

Abstract

For the gravitational wave model based on the type III Shapovalov wave space-time, test particle trajectories and the exact solution of geodesic deviation equations for the Bianchi type VII universe are obtained. Based on the found 4-vector of deviation, tidal accelerations in a gravitational wave are calculated. For the obtained solution in a privileged coordinate system, an explicit form of transformations into a synchronous reference system is found, which allows time synchronization at any points of space-time with separation of time and spatial coordinates. The synchronous reference system used is associated with a freely falling observer on the base geodesic. In a synchronous coordinate system, an explicit form of the gravitational wave metric, a 4-vector of geodesic deviation, and a 4-vector of tidal accelerations in a gravitational wave are obtained. The exact solution describes a variant of the primordial gravitational wave. The results of the work can be used to study the plasma radiation generated by tidal accelerations of a gravitational wave.