Aspects of spherically symmetric cosmological models.
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Date
1998
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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.
Description
Thesis (M.Sc.)-University of Natal, Durban, 1998.
Keywords
General relativity (Physics), Space and time., Cosmology., Symmetry (Physics), Theses--Mathematics., Einstein field equations--Numerical solutions.