Details of the group‐theoretical method for the separation of tensor equations in a homogeneous space are given. As illustrations, the vector and tensor harmonics in a SO(3)‐homogeneous space are constructed, with applications to the study of electromagnetic and gravitational perturbations in the mixmaster universe.

Separation of tensor equations in a homogeneous space by group theoretical methods

Inhomogeneous mixmaster universes: Some exact solutions

This paper reviews recent applications of the Einstein-Rosen type space-times to some problems of modern cosmology. An extensive overview of inhomogeneous universes filled with gravitational waves, classical fields, and relativistic fluids is given. The dynamics of primordial inhomogeneities, such as gravitational and matter waves and shocks, their interactions, and the global evolution of the models considered, is presented in detail.

The Einstein-rosen Gravitational Waves and Cosmology

Prinzipielles zur allgemeinen Relativitätstheorie

An exact analytical model of the process of collision and nonlinear interaction of gravitational and/or electromagnetic soliton wave and strong non-soliton electromagnetic traveling wave of arbitrary profile propagating in the expanding universe (the symmetric Kasner spacetime) is presented. In contrast to intuitive expectations that rather strong traveling waves can destroy the soliton, it occurs that the soliton survives during its interaction with electromagnetic wave of arbitrary amplitude and profile, but its parameters begin to evolve under the influence of this interaction. If a traveling electromagnetic wave possesses a finite duration, the soliton parameters after interaction take constant values again, but these values in general are different from those before the interaction. Based on exact solutions of Einstein - Maxwell equations, our model demonstrates a series of nonlinear phenomena, such as (a) creation of gravitational waves in the collision of two electromagnetic waves, (b) creation of electromagnetic soliton wave in the collision of gravitational soliton with traveling electromagnetic wave, (c) scattering of a part of soliton wave in the direction of propagation of traveling electromagnetic wave, (d) quasiperiodic oscillating character of fields in the wave interaction region and multiple mutual transformations of gravitational and electromagnetic waves in this region. The figures illustrate these features of nonlinear wave interactions in General Relativity.

Nikos Batakis

Papers

Closed anisotropic cosmological models.