Stationary model of the Universe with torsion

Abstract

On a four-dimensional pseudo-Riemannian manifold with the metric of a stationary model of the Universe, we construct a Riemann-Cartan structure with the automorphism group of maximum dimension. The torsion tensor of this structure is the sum of two parts: semisymmetric, aspiring to geometrization of the spin density of matter, and skew-symmetric, determining the torsion of a spatial section. We give a geometric interpretation of the spatial section torsion. We prove that the maximum dimension of the Lie group of automorphisms of a Riemann-Cartan space-time manifold with a semisymmetric or skewsymmetric connection is seven.