Thesis (Ph. D.)--Columbia University, 1927. / Without thesis note. Thesis note on label mounted on t.p. Bibliography: p. [236]-250.

Thesis (Ph. D.)--West Virginia University, 1999. / Title from document title page. Document formatted into pages; contains ix, 223 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 214-223) and index.

Thesis (Ph. D.)--Columbia University, 1927. / Without thesis note. Thesis note on label mounted on t.p. Bibliography: p. [236]-250.

Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Vita. Includes bibliographical references (leaf 60). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Vita. Includes bibliographical references (leaf 60). Also available on the Internet.

Thesis (M.S.)--California Polytechnic State University, 2009. / Mode of access: Internet. Title from PDF title page; viewed on September 28, 2009. Major professor: Dr. Eric A. Mehiel. "Presented to the faculty of California Polytechnic State University, San Luis Obispo." "In partial fulfillment of the requirements for the degree [of] Master of Science in Aerospace Engineering." "September 2009." Includes bibliographical references (p. 52).

Orientador: José Geraldo Pereira / Banca: Ruben Aldrovandi / Banca: Victor de Oliveira Rivelles / Banca: José Abdalla Helaÿel-Neto / Banca: José Wadih Maluf / Resumo: Na primeira parte da tese é feito um estudo dos fundamentos do equivalente teleparalelo da Relatividade Geral. Usando o fato que esse modelo corresponde a uma teoria de gauge para o grupo das translações, obtemos primeiramente a corrente de gauge representando a densidade de energia-momento do campo gravitacional, a qual se verifica ser um tensor verdadeiro. Sua relação com a expressão de Moller para o pseudo-tensor energia-momento canônico é também obtida. Então, para que resulte completamente equivalente com a Relatividade Geral, uma nova expressão para a conexão de spin teleparalela é proposta. Na segunda parte da tese, adotando-se a estrutura de gauge do Teleparalelismo como paradigma, desenvolvemos a versão teleparalela da teoria de Kaluza-Klein não- Abeliana. Nessa teoria, apenas o espaço interno (fibra) adquire dimensões extras, sendo o espaço-tempo mantido sempre quadri-dimensional. O processo de unificação neste formalismo resulta bem mais simples e natural do que nos modelos de Kaluza- Klein ordinários / Abstract: In the first part of the thesis, a study on the foundations of the teleparallel equivalent of General Relativity is made. Using the fact that it corresponds to a gauge theory for the translation group, we obtain first the energy-momentum gauge current of the gravitational field, which is shown to be a true tensor. Its relation to the usual expression obtained by Mpller for the canonical energy-momentum pseudo-tensor is also obtained. Then, in order to be fully equivalent with General Relativity, a new expression for the teleparallel spin connection is proposed. In the second part of the thesis, by adopting the gauge construction of teleparallel gravity as paradigm, a teleparallel version of the non-Abelian Kaluza-Klein theory is developed. In this theory, only the internai (fiber) space acquires extra dimensions, spacetime being kept always four-dimensional. The uniíication in this approach results to be much simpler and more natural than in ordinary Kaluza-Klein models / Doutor

A quantum theory of gravitation is constructed, by considering the gravitational field in the linear approximation to be a rank II tensor field, which has imposed upon it the auxiliary conditions of symmetry, transversality, and tracelessness. Extensive use is made of the close analogy between the electromagnetic field as a special case of a vector field, and the gravitational field as a special case of a tensor field. This analogy includes the necessity of introducing an indefinite metric in order to make the auxiliary conditions compatible with the commutation relations. A complete theory of gravitation must take into account the gravitating nature of gravitation and hence must be a nonlinear theory. A method proposed by Gupta of iterating the linear field equations for this purpose is investigated, and it is shown that this method fails, because the Lagrangian for the second order equations does not exist. An alternative method of iteration is proposed which avoids this problem, and which yields a functional equation for the Lagrangian of the full nonlinear theory. Finally, the problem of photon-photon scattering due to the gravitational interaction is investigated. This is done by constructing an interaction Hamiltonian by using the principle of the compensating field and then applying the standard methods of quantum electrodynamics. It is found that for sufficiently high frequencies this process dominates the purely electrodynamic scattering of photons by photons. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The objective of this Thesis is to explore Poincaré Gauge theories of gravity and expose some contributions to this field, which are detailed below. Moreover, a novel ultraviolet non-local extension of this theory shall be provided, and it will be shown that it can be ghost- and singularity-free at the linear level. First, we introduce some fundamentals of differential geometry, base of any gravitational theory. We then establish that the affine structure and the metric of the spacetime are not generally related, and that there is no physical reason to impose a certain affine connection to the gravitational theory. We review the importance of gauge symmetries in Physics and construct the quadratic Lagrangian of Poincaré Gauge gravity by requiring that the gravitational theorymust be invariant under local Poincaré transformations. We study the stability of the quadratic Poincaré Gauge Lagrangian, and prove that only the two scalar degrees of freedom (one scalar and one pseudo-scalar) can propagate without introducing pathologies. We provide extensive details on the scalar, pseudo-scalar, and bi-scalar theories. Moreover, we suggest how to extend the quadratic Poincaré Gauge Lagrangian so that more modes can propagate safely. We then proceed to explore some interesting phenomenology of Poincaré Gauge theories. Herein, we calculate how fermionic particles move in spacetimes endowed with a nonsymmetric connection at first order in the WKB approximation. Afterwards, we use this result in a particular black-hole solution of Poincaré Gauge gravity, showing that measurable differences between the trajectories of a fermion and a boson can be observed. Motivated by this fact, we studied the singularity theorems in theories with torsion, to see if this non-geodesical behaviour can lead to the avoidance of singularities. Nevertheless, we prove that this is not possible provided that the conditions for the appearance of black holes of any co-dimension are met. In order to see which kind Black Hole solutions we can expect in Poincaré Gauge theories, we study Birkhoff and no-hair theorems under physically relevant conditions. Finally, we propose an ultraviolet extension of Poincaré Gauge theories by introducing non-local (infinite derivatives) terms into the action, which can ameliorate the singular behaviour at large energies. We find solutions of this theory at the linear level, and prove that such solutions are ghost- and singularity-free. We also find new features that are not present in metric Infinite Derivative Gravity.

Modern cosmological theory is based on the Friedmann-Robertson-Walker (FRW) metric. Often written in terms of co-moving coordinates, this well-known solution to Einstein's equations owes its elegant and highly practical formulation to the Cosmological principal and Weyl's postulate, upon which it is founded. But there is physics behind such symmetries, and not all of it has yet been recognized. In this paper, we derive the FRW metric coefficients from the general form of the spherically-symmetric line element, and demonstrate that, because the co-moving frame also happens to be in free fall, the symmetries in FRW are valid only for a medium with zero active mass. In other words, the spacetime of a perfect fluid in cosmology may be correctly written as FRW only when its equation-of-state is $\rho+3p=0$, in terms of the {\it total} pressure $p$ and {\it total} energy density $\rho$. There is now compelling observational support for this conclusion, including the Alcock-Paczy\'nski test, which shows that only an FRW cosmology with zero active mass is consistent with the latest model-independent Baryon Acoustic Oscillation data.