Gladush V. Geometrical methods in the theory of relativistic configurations

The physical processes in the astrophysical and cosmological configurations in general relativity and multidimensional theories of gravitation. Differential-geometry formalism of the theory of relativistic configurations is developed. The models of charged dust spheres and the gravitational collapse are built. The methods of the modern differential geometry, theory of tensor representations group and canonical transformations, semiclassical methods are used. Formalism of the split theory and unimodular symmetry of spherically-symmetric spaces, stability theory of static spheres of the charged dust, theory of dust spherical shells and their semiclassical treatment, dynamic realization of the Kaluza-Klein conditions, generalized Casimir operator are elaborated. The exact solutions for charged dust configurations are obtained. The developed methods and obtained results can be used for the construction of models of relativistic objects and cosmological models on the basis of exact solutions of the Einsteinequations and their multidimensional generalizations.