Secondary gravitational waves against a strong gravitational wave in the Bianchi VI universe

TL;DR

This paper develops an analytical model for secondary gravitational waves generated in the Bianchi VI universe using a proper-time method, revealing conditions for the stability of these waves.

Contribution

It introduces a novel proper-time approach to construct explicit analytical models of secondary gravitational waves in a Bianchi VI universe, including stability analysis.

Findings

Analytical solutions for secondary gravitational waves are derived.

Conditions for the stability of perturbative solutions are identified.

Explicit differential equations governing the wave perturbations are obtained.

Abstract

A proper-time method for constructing models of dynamic gravitational-wave fields is presented. Using the proper-time method, analytical (not numerical) models of secondary gravitational waves are constructed as perturbative solutions of linearized field equations against the background of the exact wave solution of Einstein's equations for the vacuum in the Bianchi VI universe in a privileged wave coordinate system. Relations for the proper time of test particles against the background of a strong gravitational wave are used. The analytical form of the metric components for secondary gravitational waves is found from compatibility conditions for the field equations. From the field equations, an explicit form of ordinary differential equations and their solutions is obtained for functions included in small corrections to the metric for secondary gravitational waves. It is shown that there exists a continuum of gravitational wave parameters for which the perturbative solutions are stable.