# Spherically symmetric cosmological solutions.

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## Date

1996

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## Abstract

This thesis examines the role of shear in inhomogeneous spherically symmetric spacetimes
in the field of general relativity. The Einstein field equations are derived for
a perfect fluid source in comoving coordinates. By assuming a barotropic equation
of state, two classes of nonaccelerating solutions are obtained for the Einstein field
equations. The first class has equation of state p = ⅓µ and the second class, with
equation of state p = µ, generalises the models of Van den Bergh and Wils (1985).
For a particular choice of a metric potential a new class of solutions is found which
is expressible in terms of elliptic functions of the first and third kind in general. A
class of nonexpanding cosmological models is briefly studied. The method of Lie
symmetries of differential equations generates a self-similar variable which reduces
the field and conservation equations to a system of ordinary differential equations.
The behaviour of the gravitational field in this case is governed by a Riccati equation
which is solved in general. Another class of solutions is obtained by making an ad
hoc choice for one of the gravitational potentials. It is demonstrated that for a stiff
fluid a particular case of the generalised Emden-Fowler equation arises.

## Description

Thesis (Ph.D.)-University of Natal, Durban, 1996.

## Keywords

Einstein field equations--Numerical solutions., General relativity (Physics), Space and time., Theses--Mathematics.