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We study the evolution of Bianchi-I space-times filled with a global unidirectional electromagnetic field Fµν interacting with a massless scalar dilatonic field according to the law Ψ(φ)F µν Fµν where Ψ(φ) > 0 is an arbitrary function. A qualitative study, among other results, shows that (i) the volume factor always evolves monotonically, (ii) there exist models becoming isotropic at late times and (iii) the expansion generically starts from a singularity but there can be special models starting from a Killing horizon preceded by a static stage. All three features are confirmed for exact solutions found for the usually considered case Ψ = e 2λφ , λ = const . In particular, isotropizing models are found for |λ| > 1/ √ 3 . In the special case |λ| = 1 , which corresponds to models of string origin, the string metric behaviour is studied and shown to be qualitatively similar to that of the Einstein frame metric.

Self-consistent solutions to interacting spinor and scalar field equations in General Relativity are studied for the case of Bianchi type-I space-time filled with perfect fluid. The initial and the asymptotic behavior of the field functions and the metric one has been thoroughly studied. PACS 04.20.Jb

Self-consistent solutions to nonlinear spinor field equations in General Relativity have been studied for the case of Bianchi type-I space-time filled with perfect fluid. The initial and the asymptotic behavior of the field functions and the metric one has been thoroughly studied. It should be emphasized the absence of initial singularity for some types of solutions and also the isotropic mode of space-time expansion in some special cases. PACS 04.20.Jb

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