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In Part I, spherically symmetric solutions of Rastall's 1971 gravitational field equations for empty space-time are examined. One static solution is found to be just a static spherically symmetric Newtonian metric; i.e., the metric of Rastall's 1968 scalar theory of gravity. However, there are other solutions which satisfy the same boundary conditions at spatial infinity. It is observed that the time-like vector field n[formula omitted] appearing in the field equations is not uniquely defined when the metric is assumed to be spherically symmetric. Part I concludes with a discussion of the effects of this ambiguity upon the solutions of the field equations. Part II is a discussion of an alternative procedure for generalizing Rastall's 1968 theory of gravity. The new, generalized Newtonian metric is assumed to satisfy the linearized vacuum field equations of General Relativity in the weak-field limit. The quantities from which generalized Newtonian metrics are constructed are then found to exhibit wave-like behavior. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

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Durante os últimos 90 anos temos visto o grande esplendor que a teoria da relatividade geral de Einstein alcançou em suas diversas previsões. Esta dissertação é um estudo a respeito desta teoria e suas extrapolações. Falaremos de início acerca da primeira solução das equações de Einstein para buracos negros obtida por Karl Schwarzschild em 1916: o buraco negro esfericamente simétrico e sem carga. Trataremos das possíveis órbitas neste tipo de solução bem como de perturbações gravitacionais e escalares. Ainda utilizando a solução de Schwarzschild, adentraremos os tópicos desenvolvidos recentemente em um tratamento semi-clássico da relatividade: a termodinâmica dos buracos negros. Posteriormente estudaremos as novas teorias com base na relatividade geral, que resolvem o problema da hierarquia buscando por dimensões extras em nosso Universo. Em tal contexto analisamos por exemplo como se comportam os buracos negros nestes Universos com mais do que 4 dimensões. Porém, estudamos perturbações gravitacionais em uma corda negra chegando a averiguar a presença de uma instabilidade para modos com comprimento de onda maiores do que o horizonte da corda (em uma aproximação linear), e demonstramos que em uma das possíveis soluções do problema da Hierarquia (Universos de Randall Sundrum) não existem atalhos gravitacionais mesmo para branas não planas (extrapolação dos Universos de Randall-Sundrum). / Over the last 90 years Einstein`s Theory of General Relativity has had a tremendous success in all its predictions. This dissertation is concerned with the study of this theory and its extrapolations. We begin with the first solution of the Einstein equations for black holes obtained by Karl Schwarzschild at 1916: the spherically symmetric black hole without charge, obtaining the orbits and the scalar and gravitational perturbations around the metric. We also consider the recent developments in black hole thermodynamics via a semiclassical approach to the theory. Subsequently, we study the new theories based on general relativity extrapolations, which solve the hierarchy problem proposing extra dimensions in our Universe. In this context we analyze for example the behavior of black holes in Universes with more than 4 dimensions. Finally, we study the gravitational perturbations in a black string showing the presence of unstable modes with wave length bigger than the black string horizon. We also show that in one of the possible Universes which solve the hierarchy problem there are no gravitational shortcuts even for non-at branes (an extrapolation of Randall-Sundrum Universes).

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Thesis (Ph. D.)--University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (Mar. 1, 2007). Vita. Includes bibliographical references.

Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Berlin, 1912. / Vita. Includes bibliographical references.

Proefschrift--Utrecht. / "Stellingen": [3] p. inserted. Vita. Erratum slip inserted. Bibliography: p. 140-146.

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (leaves 178-181).

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