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

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.

17 pages

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