Thesis--Tübingen. / Vita. Includes bibliographical references (p. 82-90).

Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 110-116). Available also in a digital version from Dissertation Abstracts.

Thesis (M.F.A.)--West Virginia University, 2003. / Title from document title page. Document formatted into pages; contains iv, 17 p. : col. ill. Vita. Includes abstract. Includes bibliographical references (p. 15).

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While the groundbreaking insights that contemporary theorists have formulated with regards to space---as a multiplicity without essence, as an active event, and as inseparable from subjectivity, power, Otherness and time---have ostensibly purged it of its traditional understanding as absolute, a specific visuality characteristic of Cartesian perspectivalism remains privileged in its theorization which force it to remain so. While the complexity of space cannot be recovered from an abstract contemplation of its visual geometry in a way that reflects these contemporary concerns, there have unfortunately been relatively few attempts to imagine space away from the visual in a way that challenges its traditional absoluteness. To this end, it is argued that because sound and music contain implicit and explicit spatialities, the sonic represents a rich and unexplored area from which to imagine a radical non-visual space that discursively organizes space according to a different economy through which to challenge its assumed visuality. And yet, even when space has been approached through sound, there is a tendency to exteriorize sound into an object or a set of practices that robs it of its defining quality---its own "soundfulness". By breaking down those factors that are considered salient to how space is conceived today along sonic rather than visual lines, the argument is made that the "soundfulness" of sound's physical properties gives it a complex texture of excess that is corporealized within the body and forwards the philosophical possibility of unfolding the spatiality of sound according to vectors beyond the visible in a way that, while reflecting contemporary concerns, prevents its return to absoluteness. To take seriously this "soundfulness" thus allows us to recuperate the sonic as a philosophical and political way of experiencing and knowing the world, including that of space. The arguments, as well as being drawn from the insights of contemporary spatial theory, the physics of sound, the phenomenology of listening, rhizomatic and feminist theory, quantum mechanics and musicology, will be explained through an understanding of space as sound and exemplified in The Disintegration Loops, a post-minimalist musical piece by sonic artist William Basinski.

In this thesis we study the conformal symmetries in two locally rotationally symmetric spacetimes and the homothetic symmetries of a Bianchi I spacetime. The conformal Killing equation in a class AIa spacetime (MacCallum 1980), with a G4 of motions, is integrated to obtain the general solution subject to integrability conditions. These conditions are comprehensively analysed to determine the restrictions on the metric functions. The Killing vectors are contained in the general conformal solution. The homothetic vector is obtained and the explicit functional dependence of the metric functions determined. The class AIa spacetime does not admit a nontrivial special conformal factor. We also integrate the conformal Killing equation in the anisotropic locally rotationally symmetric spacetime of class A3 (MacCallum 1980), with a G4 of motions, to obtain the general conformal Killing vector and the conformal factor subject to integrability conditions. The Killing vectors are obtained as a special case from the general conformal solution. The homothetic vector is found for a nonzero constant conformal factor. The explicit functional form of the metric functions is determined for the existence of this homothetic vector. The spatially homogeneous and anisotropic A3 spacetime also does not admit a nontrivial special conformal vector. In the Bianchi I spacetime, with a G3 of motions, the conformal Killing equation is integrated for a constant conformal factor to generate the homothetic symmetries. The integrability conditions are solved to determine the functional dependence of the three time-dependent metric functions. / Thesis (M.Sc.)-University of Natal, Durban, 1991.

In this dissertation we consider spherically symmetric gravitational fields that arise in relativistic astrophysics and cosmology. We first present a general review of static spherically symmetric spacetimes. aand highlight a particular class of exact solutions of the Einstein-Maxwell system for charged spheres. In the case of shear-free spacetimes with heat flow, the integration of the system is reduced to solving the condition of pressure isotropy. This condition is a second order linear differential equation with variable coefficients. By choosing particular forms for the gravitational potentials, sev-eral classes of new solutions are generated. We regain known solutions corresponding to coniformal flatness when tidal forces are absent. We also consider expanding, accelerating and shearing models when the heat flux is not present. A new general class of models is found. This new class of shearing solutions contains the model of Maharaj et al (1993) when a parameter is set to zero. Our new solution does not contain a singularity at the stellar centre, and it is therefore useful in modelling the interior of stars. Finally, we demonstrate that the shearing models obtained by Markund and Bradley (1999) do not satisfy the Einstein field equations. / Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2007.

1's) representing the points of the primary space fails to be complete; but it can be completed to give a 4- dimensional family, effecting a unique embedding of the original 3-fold in a 4-fold with conformal structure, of which the conformal curvature is selfdual, in such a way that the induced conformal structure is the original one and such that the conformal torsion is related to the second conformal fundamental form of the hypersurface in a canonical linear fashion. In any case, the small deformations of the complex structure of the space of null geodesies correspond precisely to the small deformations of the conformal connexion. It is shown that a space of torsion-free null geodesies admits a holomorphic contact structure, and that conversely, for n ≥ 4, the admission of a contact structure forces the conformal torsion to vanish; for n=3, the contact form constructs automatically a unique metric on the ambient 4-fold in the previously constructed self-dual conformal class which solves Einstein's equations with cosmological constant 1 and blov/s up on the 3-fold, which is a general umbilic hypersurface. These results are in turn used to show that a real-analytic 3-fold with real-analytic positive definite conformal structure and a real-analytic symmetric form of conformal weight 1 can be embedded (in a locally unique fashion) in a real-analytic 4-fold with positive-definite conformal structure for which the conformal curvature is self-dual in such a way as to realize the given structures as the first and second conformal fundamental forms of the hypersurface; and it is shown that a real analytic 3-fold with positivedefinite conformal bounds a locally unique positive-definite solution of Einstein's equations with cosmological constant -1 as its umbilic conformal infinity. By contrast, these results fail when "real-analytic" is replaced by "smooth".