Burton, Howard Steven2006-07-282006-07-2819991999http://hdl.handle.net/10012/361This thesis involves a rigorous treatment of the Palatini Variational Principle of gravitational actions in an attempt to fully understand the role of the connection in such theories. After a brief geometrical review of affine connections, we examine N-diensional dilatonic theories via the Standard Palatini principle in order to highlight the potential differences arising in the dynamics of theories obtained by utilizing the Hilbert and Palatini formalisms. We then develop a more generalized N-dimensional, torsion-free, Einstein-Hilbert-type action which is shown to give rise to Einsteinian dynamics but can be made, for certain choices of the associated arbitrary parameters, to yield either weak constraints or no constraints on the connection r . The latter case is referred to as a "maximally symmetric" action. In the following Chapter this analysis is extended to the realm of a potentially non-vanishing torsion tensor, where it is seen that such actions do not, in general, lead to Einsteinian dynamics under a Palatini variation. Following another brief geometrical review, which highlights some elements of fibre bundle theory appropriate to our later analysis, we examine the so-called Palatini Tetrad formalism and show that it must be modified for a proper Palatini variation - i.e. to not assume anything a priori about the relevant connection. We then analyze this modified approach from a geometrical perspective and show that, for the torsion-free case at least, a proper treatment of the Palatini Tetrad procedure is equivalent to the "maximally symmetric" case alluded to earlier.application/pdf5319813 bytesapplication/pdfenCopyright: 1999, Burton, Howard Steven. All rights reserved.Harvested from Collections CanadaDoctoral Thesis