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Spherically symmetric cosmological solutions.

dc.contributor.advisorMaharaj, Sunil Dutt.
dc.contributor.authorGovender, Jagathesan.
dc.date.accessioned2012-01-19T07:38:51Z
dc.date.available2012-01-19T07:38:51Z
dc.date.created1996
dc.date.issued1996
dc.descriptionThesis (Ph.D.)-University of Natal, Durban, 1996.en
dc.description.abstractThis 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.en
dc.identifier.urihttp://hdl.handle.net/10413/4842
dc.language.isoenen
dc.subjectEinstein field equations--Numerical solutions.en
dc.subjectGeneral relativity (Physics)en
dc.subjectSpace and time.en
dc.subjectTheses--Mathematics.en
dc.titleSpherically symmetric cosmological solutions.en
dc.typeThesisen

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