Aspects of spherically symmetric cosmological models.

Abstract

In this thesis we consider spherically symmetric cosmological models when the shear is nonzero and also cases when the shear is vanishing. We investigate the role of the Emden-Fowler equation which governs the behaviour of the gravitational field. The Einstein field equations are derived in comoving coordinates for a spherically symmetric line element and a perfect fluid source for charged and uncharged matter. It is possible to reduce the system of field equations under different assumptions to the solution of a particular Emden-Fowler equation. The situations in which the Emden-Fowler equation arises are identified and studied. We analyse the Emden-Fowler equation via the method of Lie point symmetries. The conditions under which this equation is reduced to quadratures are obtained. The Lie analysis is applied to the particular models of Herlt (1996), Govender (1996) and Maharaj et al (1996) and the role of the Emden-Fowler equation is highlighted. We establish the uniqueness of the solutions of Maharaj et al (1996). Some physical features of the Einstein-Maxwell system are noted which distinguishes charged solutions. A charged analogue of the Maharaj et al (1993) spherically symmetric solution is obtained. The Gutman-Bespal'ko (1967) solution is recovered as a special case within this class of solutions by fixing the parameters and setting the charge to zero. It is also demonstrated that, under the assumptions of vanishing acceleration and proper charge density, the Emden-Fowler equation arises as a governing equation in charged spherically symmetric models.