Exact solutions for spherical relativistic models.
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Date
2011
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Abstract
In this thesis we study relativistic models of gravitating
uids with heat
ow and electric
charge. Firstly, we derive the model of a charged shear-free spherically symmetric cosmological
model with heat
ow. The solution of the Einstein-Maxwell equations of the system
is governed by the pressure isotropy condition. This condition is a highly nonlinear partial
di erential equation. We analyse this master equation using Lie's group theoretic approach.
The Lie symmetry generators that leave the equation invariant are found. We provide exact
solutions to the gravitational potentials using the rst symmetry admitted by the equation.
Our new exact solutions contain the earlier results of Msomi et al (2011) without charge.
Using the second symmetry we are able to reduce the order of the master equation to a rst
order highly nonlinear di erential equation.
Secondly, we study a shear-free spherically symmetric cosmological model with heat
ow
in higher dimensions. We establish the Einstein eld equations and nd the governing
pressure isotropy condition. We use an algorithm due to Deng (1989) to provide several
new classes of solutions to the model. The four-dimensional case is contained in our general
result. Solutions due to Bergmann (1981), Maiti (1982), Modak (1984) and Sanyal and Ray
(1984) for the four-dimensional case are regained. We also establish a new class of solutions
that contains the results of Deng (1989) from four dimensions.
Description
Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2011.
Keywords
Relativistic quantum theory., Symmetric functions., Differential equations., Theses--Mathematics.