Cosmologies with a magnetic field, dust, and Lambda

We investigate exact solutions of the Einstein-Maxwell equations with the cosmological constant where the source of the gravitational field consists of a magnetic field and dust. In particular, we restrict our study to the case of Bianchi type III models. All these solutions either start with a singularity and then expand, or they are initially collapsing and end at a singularity. We discuss the physical meaning of the parameters appearing in the metrics and examine the possible subcases and the relative importance of the dust and the magnetic field as we approach the singularity.