Description of open cosmological models with matter by harmonic functions

Abstract

An approach is considered to a description of conformally flat open models in general relativity with the energy-momentum tensor of an ideal fluid for an equation of state of the type p=β · ε. In the approximation of rational β, in order to describe such models by harmonic functions it is necessary to increase the dimensionality of the spacelike hypersurface N of 4-dimensional spacetime. A similarity is pointed out between N and N·β and the orbital and magnetic numbers in quantum mechanics. It is shown that a new variable can be introduced such that the problem is reduced to the equivalent problem of planetary model of a hydrogen-like atom.