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Thesis (Ph. D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 1992. / Includes bibliographical references.

We investigate techniques to generate new classes of exact solutions to the Einstein- Maxwell field equations which represent the gravitational field of charged perfect fluid spherically symmetric distributions of matter. Historically, a large number of solutions have been proposed but only a small number have been demonstrated to satisfy elementary conditions for physical acceptability. Firstly we examine the case of the constant density and constant electric field charged fluid sphere and show empirically that such configurations of matter are unlikely to exist as basic physical requirements are violated. We then make an ansatz relating the fluid's electric field intensity to one of the gravitational potentials thereby simplifying the system of partial differential equations. This prescription yields an algorithmic process to generate new classes of exact solutions. We present a number of new solutions and comment on their viability as stellar models. Graphical plots generated by symbolic software of the main dynamical and geometrical quantities verify that one of our models is suitable to represent a physically relevant distribution of charged matter in the form of a spherical shell. In particular, positive definiteness of energy density and pressure are guaranteed, a pressure free hypersurface denoting the boundary of the star exists, the sound speed is shown to be sub-luminal and the energy conditions are satisfied everywhere in the interior of the star. / Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2012.

In this thesis a number of problems concerning proper curvature collineations, proper Weyl collineations and projective vector fields will be considered. The work on the above areas can be summarised as: (i) A study of proper curvature collineations in plane symmetric static, spherically symmetric static and Bianchi type <I>I</I> spacetimes will be presented by considering the rank of their 6 x 6 Riemann tensors and using a theorem which eliminates those space-times where proper curvature collineations can not exist; (ii) A study of proper Weyl collineations is given by using the algebraic classification and associated rank of the Weyl tensor and using a theorem similar to that used in (i); (iii) A technique is developed to study projective vector fields in the Friedmann Robertson-Walker models and plane symmetric static spacetimes; (iv) The situations when conformally flat spacetimes admit proper curvature collineations are fully explored.

Includes bibliographical references / vi, 128 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 1992

Thesis (Ph. D.)--University of Oregon, 2007. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 95-98). Also available for download via the World Wide Web; free to University of Oregon users.

In this thesis, we study the odd solution of the linearlized Einstein equation on the Schwarzschild background and in the harmonic gauge. With the aid of Regge-Wheeler quantities, we are able to estimate the odd part of Lichnerowicz d'Alembertian equation. In particular, we prove the solution decays to a linearlized Kerr solution except for the angular mode l=2.

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (p. 205-211).

We study the evolution of shear-free spherically symmetric charged fluids in general relativity. This requires the analysis of the coupled Einstein-Maxwell system of equations. Within this framework, the master field equation to be integrated is yxx = f(x)y2 + g(x)y3 We undertake a comprehensive study of this equation using a variety of ap- proaches. Initially, we find a first integral using elementary techniques (subject to integrability conditions on the arbitrary functions f(x) and g(x)). As a re- sult, we are able to generate a class of new solutions containing, as special cases, the models of Maharaj et al (1996), Stephani (1983) and Srivastava (1987). The integrability conditions on f(x) and g(x) are investigated in detail for the purposes of reduction to quadratures in terms of elliptic integrals. We also obtain a Noether first integral by performing a Noether symmetry analy- sis of the master field equation. This provides a partial group theoretic basis for the first integral found earlier. In addition, a comprehensive Lie symmetry analysis is performed on the field equation. Here we show that the first integral approach (and hence the Noether approach) is limited { more general results are possible when the full Lie theory is used. We transform the field equation to an autonomous equation and investigate the conditions for it to be reduced to quadrature. For each case we recover particular results that were found pre- viously for neutral fluids. Finally we show (for the first time) that the pivotal equation, governing the existence of a Lie symmetry, is actually a fifth order purely differential equation, the solution of which generates solutions to the master field equation. / Thesis (Ph.D.)-University of KwaZulu-Natal, Westville, 2011.