Linear perturbations of an exact gravitational wave in the Bianchi IV universe

TL;DR

This paper develops a perturbative analytical model of gravitational waves in a Bianchi IV universe using the proper-time method, demonstrating the stability of these solutions.

Contribution

It introduces a new perturbative approach to gravitational waves in anisotropic universes and provides explicit analytical solutions and stability analysis.

Findings

Analytical solutions for gravitational wave components were derived.

The stability of the perturbative solutions was proven.

The stability of the exact gravitational wave solution in Bianchi IV universe was demonstrated.

Abstract

The proper-time method for constructing perturbative dynamical gravitational fields is presented. Using the proper-time method, a perturbative analytical model of gravitational waves against the backdrop of an exact wave solution of Einstein's equations in a Bianchi IV universe is constructed. To construct the perturbative analytical wave model a privileged wave coordinate system and a synchronous time function associated with the proper time of an observer freely moving in a gravitational wave were used. Reduction of the field equations, taking into account compatibility conditions, reduces the mathematical model of gravitational waves to a system of coupled ordinary differential equations for functions of the wave variable. Analytical solutions for the components of the gravitational-wave metric have been found. The stability of the resulting perturbative solutions is proven. The stability of the exact solution for a gravitational wave in the anisotropic Bianchi IV universe is demonstrated.