Communications in Mathematical Physics

, Volume 26, Issue 1, pp 24–38 | Cite as

Gravitational fields with groups of motions on two-dimensional transitivity hypersurfaces in a model with matter and a magnetic field

  • I. S. Shikin
Article

Abstract

For gravitational fields with metrics which admit of groups of motions multiply — transitive on 2-dimensional space-like invariant varieties, the exact solutions of the Einstein gravitational equations are given for the case when the sources of the gravitational field are dust-like matter and a magnetic field. A magnetic field is orientated along a direction orthogonal to transitivity hypersurface. The solutions contain arbitrary functions. In the case of transitivity hypersurface of positive curvature and in the absence of a magnetic field, the solution is reduced to the Tolman spherically symmetric solution for dust-like matter. The conditions are studied under which the solutions with a magnetic field become asymptotically isotropic and approach the flat and the open Friedmann models. The case of transitivity hypersurfaces with signature (+ −) is also considered.

Keywords

Magnetic Field Neural Network Statistical Physic Exact Solution Complex System 

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Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • I. S. Shikin
    • 1
  1. 1.Moscow State UniversityMoscowUSSR

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