A class of exact solutions of certain classical field equations in general relativity

Abstract

This paper deals with certain model statical universes representing exact solutions of some field equations in general relativity. Three universes of this type are discussed. They correspond to combinations of gravitation respectively with (i) electromagnetic field, (ii) scalar or pseudo-scalar field, (iii) Maxwell-Dirac field. Such statical solutions are possible in the first two cases only if mass density and charge density are equal in magnitude, and in the third case only if mass and charge are equal in magnitude, so that matter is in equilibrium under the action of gravitation and other forces. The field equations, in this work, are classical in the sense that no second quantization is involved.