In this thesis we study spherically symmetric spacetimes related to the Einstein field equations. We consider only neutral matter and apply the Einstein field equations with isotropic pressures. Our object is to model relativistic stellar systems. We express the Einstein field equations and the condition of pressure isotropy in terms of Schwarzschild coordinates and isotropic coordinates. For Schwarzschild coordinates we consider the transformations due to Buchdahl (1959), Durgapal and Bannerji (1983), Fodor (2000) and Tewari and Pant (2010). The condition of pressure isotropy is integrated and new exact solutions of the field equations are obtained utilizing the transformations of Buchdahl (1959) and Tewari and Pant (2010). These exact solutions are given in terms of elementary functions. For isotropic coordinates we can express the condition of pressure isotropy as a Riccati equation or a linear equation. An algorithm is developed that produces a new solution if a particular solution is known. The transformations reduce to a nonlinear Bernoulli equation in most instances. There are fundamentally three new classes of solutions to the condition of pressure isotropy. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2011.

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. / Thesis (M.Sc.)-University of Natal, Durban, 1998.

The content of this thesis is two-fold. The first part takes the form of an essay while the second part presents a theoretical project for an architectural installation. Using these two modes as different ways to address similar issues, the present work proposes to question the instrumentalisation of geometry in today's architectural practice. The work of Lewis Carroll (Charles L. Dodgson) and, more specifically, his masterpiece, Alice's Adventures in Wonderland, will be approached and interpreted in order to observe the participation of geometry---of Euclidean geometry---in our understanding of the notions of space and time, and to reveal their paradoxical aspect. The aim is to explore how geometry, language and nonsense bear intimate connections to our perception of space and time. Once revealed, these connections will enable us to address the following question: can architecture be comprehended and experienced as an event?

This study provides a framework using matrices that address three main issues. First of all, the matrices are used to integrated physical needs that compose human systems in an attempt to reduce the human impact. Secondly, the matrices are used to develop a higher integration of time allowing the user to apply time to a wide variety of needs that contribute to a high quality of life. Lastly the matrices are used to integrate the aspects of space with the aspects of time. This shows that the whole, time and space, is greater than the sum of the parts. I pursued this study in an attempt to further define sustainable design. The application of the matrices was practiced in a design competition for urban sustainability. / Department of Architecture

In this thesis we study classes of static spherically symmetric spacetimes admitting a perfect fluid source, electromagnetic fields and anisotropic pressures. Our intention is to generate exact solutions that model the interior of dense, relativistic stars. We find a sufficient condition for the existence of series solutions to the condition of pressure isotropy for neutral isolated spheres. The existence of a series solution is demonstrated by the method of Frobenius. With the help of MATHEMATICA (Wolfram 1991) we recovered the Tolman VII model for a quadratic gravitational potential, but failed to obtain other known classes of solution. This establishes the weakness, in certain instances, of symbolic manipulation software to extract series solutions from differential equations. For a cubic potential, we obtained a new series solution to the Einstein field equations describing neutral stars. The gravitational and thermodynamic variables are non-singular and continuous. This model also satisfies the important barotropic equation of state p = p(p). Two new exact solutions to the Einstein-Maxwell system, that generalise previous results for uncharged stars, were also found. The first of these generalises the solution of Maharaj and Mkhwanazi (1996), and has well-behaved matter and curvature variables. The second solution reduces to the Durgapal and Bannerji (1983) model in the uncharged limit; this new result may only serve as a toy model for quark stars because of negative energy densities. In both examples we observe that the solutions may be expressed in terms of hypergeometric and elementary functions; this indicates the possibility of unifying isolated solutions under the hypergeometric equation. We also briefly study compact stars with spheroidal geometry, that may be charged or admit anisotropic pressure distributions. The adapted forms of the pressure isotropy condition can be written as a harmonic oscillator equation. Two simple examples are presented. / Thesis (M.Sc.)-University of Natal, Durban, 2002.

Zugl.: Rostock, Univ., Habil.-Schr.

Thesis (Ph.D.)--University of Melbourne, School of Physics, 2001. / Typescript (photocopy). Includes bibliographical references (leaves 124-135).

Thesis (M.A.(Hons.)) -- University of Western Sydney, 2002. / "M.A. (Hons.) Communication and Media, 2002, University of Western Sydney"

Thesis (M. Arch.)--Carleton University, 2004. / Includes bibliographical references (p. 106-108). Also available in electronic format on the Internet.

Thesis (M.A.) - Carleton University, 2005. / Includes bibliographical references (p. 93-99). Also available in electronic format on the Internet.