Inhomogeneous rotating universes with closed timelike geodesics of matter

Abstract

We present a new class of inhomogeneous stationary cosmological solutions of Einstein–Maxwell equations, with rotating dust and electromagnetic fields. For a subclass of these models, the topology of the space–time manifold is S3×R, and the timelike geodesic lines of dust are closed; electromagnetic fields are necessary only to avoid matter singularities, while in the completely homogeneous limit they are essential for consistency of field equations; these electromagnetic fields have the structure of magnetic monopole fields, since the total magnetic flux across the unit 2-sphere is different from zero—that is, magnetic monopoles must be present as a source of the fields.