Thesis--Cologne. / Includes bibliographical references (p. 272-275).

Thesis (Ph. D.)--Montana State University--Bozeman, 2006. / Typescript. Chairperson, Graduate Committee: Neil J. Cornish. Includes bibliographical references (leaves 140-144).

Thesis (M.Sc.)--York University, 2004. Graduate Programme in Physics and Astronomy. / Typescript. Includes bibliographical references (leaves 126-129). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: LINK NOT YET AVAILABLE.

Astronomy with gravitational-wave observations is now a reality. Much of the theoretical research in this field falls under three broad themes: the mathematical description and physical understanding of gravitational radiation and its effects; the construction of accurate and computationally efficient waveform models for astrophysical sources; and the improved statistical analysis of noisy data from interferometric detectors, so as to extract and characterise source signals. The doctoral thesis presented in this dissertation is an investigation of various topics across these themes. Under the first theme, we examine the direct interaction between gravitational waves and electromagnetic fields in a self-contained theoretical study; this is done with a view to understanding the observational implications for highly energetic astrophysical events that radiate in both the gravitational and electromagnetic sectors. We then delve into the second theme of source modelling by developing and implementing an improved waveform model for the extreme-mass-ratio inspirals of stellar-mass compact objects into supermassive black holes, which are an important class of source for future space-based detectors such as the Laser Interferometer Space Antenna. Two separate topics are explored under the third theme of data analysis. We begin with the procedure of searching for gravitational-wave signals in detector data, and propose several combinatorial compression schemes for the large banks of waveform templates that are matched against putative signals, before studying the usefulness of these schemes for accelerating searches. After a gravitational-wave source is detected, the follow-up process is to measure its parameters in detail from the data; this is addressed as we apply the machine-learning technique of Gaussian process regression to gravitational-wave data analysis, and in particular to the formidable problem of parameter estimation for extreme-mass-ratio inspirals.

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In this dissertation, we prove a number of results regarding the conformal method of finding solutions to the Einstein constraint equations. These results include necessary and sufficient conditions for the Lichnerowicz equation to have solutions, global supersolutions which guarantee solutions to the conformal constraint equations for near-constant-mean-curvature (near-CMC) data as well as for far-from-CMC data, a proof of the limit equation criterion in the near-CMC case, as well as a model problem on the relationship between the asymptotic constants of solutions and the ADM mass. We also prove a characterization of the Yamabe classes on asymptotically Euclidean manifolds and resolve the (conformally) prescribed scalar curvature problem on asymptotically Euclidean manifolds for the case of nonpositive scalar curvatures. This dissertation includes previously published coauthored material.

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Made available in DSpace on 2014-06-11T19:25:30Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-04-29Bitstream added on 2014-06-13T20:14:00Z : No. of bitstreams: 1 savi_ll_me_ift.pdf: 313272 bytes, checksum: 728354457c79218177465f833ef56d86 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O espaço de De Sitter foi estudado pela primeira vez como a solução de vácuo da equação de Einstein com constante cosmológica. Tal visão dinâmica acerca deste espaço predomina entre os físicos ainda nos dias atuais. No entanto, do ponto de vista geométrico, o espaço de de Sitter, assim como Minkowski, é um espaço quociente. Isto significa que o espço de de Sitter pode ser construído independentemente de qualquer teoria gravitacional, sendo portanto mais fundamental do que a equação de Einstein. Consequentemente, torna-se possível construir uma relatividade especial baseada no grupo de de Sitter, que e o grupo cinemático do espaço de de Sitter. Tal teoria vem sendo proposta como generalização da relatividade restrita usual com o nome de relatividade de de Sitter. Nesta, o termo cosmológico é interpretado como uma entidade cinemática, constituindo-se num segundo parâmetro invariante, além da velocidade da luz. Pode-se entender tal modi cação da relatividade einsteniana como uma solução cinemática para o problema da energia escura. No presente texto, pretendemos delinear as propriedades cinemáticas fundamentais de tal teoria em paralelo com as da relatividade restrita usual, baseada no grupo de Poincar / The de Sitter space was rst studied as the vaccum solution of Einstein's eld equation with cosmological constant. This dynamical view of that space is still prevalent among physicists even today. Nevertheless, from the point of view of geometry, the de Sitter space, like Minkowski, is a quotient space. That means that de Sitter space may be built independently of any gravitational theory, being more fundamental than Einstein's equation. Consequently, it turns out possible to construct a special relativity based on the de Sitter group. Such theory has been proposed as a generalization of ordinary special relativity, being called de Sitter relativity. In this theory, the cosmological term is interpreted as a kinematical entity, constituting a second invariant parameter, in addition to the speed of light. Such modi cation of einstenian relativity may be understood as a kinematical solution to the \dark energy problem. In the present text, we intend to outline the fundamental kinematical properties of such a de Sitter-invariant special relativity, in parallel to those of the ordinary Poincar e-invariant special relativity

This thesis considers various aspects of general relativity in more than four spacetime dimensions. Firstly, I review the generalization to higher dimensions of the algebraic classification of the Weyl tensor and the Newman-Penrose formalism. In four dimensions, these techniques have proved useful for studying many aspects of general relativity, and it is hoped that their higher dimensional generalizations will prove equally useful in the future. Unfortunately, many calculations using the Newman-Penrose formalism can be unnecessarily complicated. To address this, I describe new work introducing a higher-dimensional generalization of the so-called Geroch-Held-Penrose formalism, which allows for a partially covariant reformulation of general relativity. This approach provides great simplifications for many calculations involving spacetimes which admit one or two preferred null directions. The next chapter describes the proof of an important result regarding algebraic classification in higher dimensions. The classification is based upon the existence of a particular null direction that is aligned with the Weyl tensor of the geometry in some appropriate sense. In four dimensions, it is known that a null vector field is such a multiple Weyl aligned null direction (WAND) if and only if it is tangent to a shearfree null geodesic congruence. This is not the case in higher dimensions. However, I have formulated and proved a partial generalization of the result to arbitrary dimension, namely that a spacetime admits a multiple WAND if and only if it admits a geodesic multiple WAND.Moving onto more physical applications, I describe how the formalism that we have developed can be applied to study certain aspects of the stability of extremal black holes in arbitrary dimension. The final chapter of the thesis has a rather different flavour. I give a detailed analysis of the properties of a particular solution to the Einstein equations in five dimensions: the Pomeransky-Sen'kov doubly spinning black ring. I study geodesic motion around this black ring and demonstrate the separability of the Hamilton-Jacobi equation for null, zero energy geodesics. I show that this unexpected separability can be understood in terms of a symmetry described by a conformal Killing tensor on a four dimensional spacetime obtained by a Kaluza-Klein reduction of the original black ring spacetime.

We develop new variational techniques, acting on classes of Lagrangians with the same functional dependence but arbitrary functional form, for the derivation of general, strongly conserved quantities, supplementing the usual procedure for deriving weak conservation laws via Noether's theorem. Using these new techniques we generate and generalize virtually all energy-momentum complexes currently known. In the process we discover and understand the reason for the difficulties associated with energy-momentum complexes in general relativity. We study a Palatini variation of a novel Lagrangian due to Nissani. We find that Nissani's principal claim, that his Lagrangian specifies Riemannian geometry in the presence of a generalized matter tensor, is not in fact justifiable, and prove that his Lagrangian is not unique. We speculate on the possibility of deriving a general-relativistic analog of Maxwell's current equation, a matter current equation, yielding an entirely new approach to the idea of energy-momentum in general relativity. We develop the SL(2,C) x U(1) spinor formalism naturally combining the gravitational and electromagnetic potentials in a single object--the spinor connection. Variably charged matter is rigourously introduced, through the use of spin densities, in the unified potential theories we develop. We generate both the Einstein-Maxwell equations and new equations. The latter generalize both the Maxwell equation and the Einstein equation which includes a new "gravitational stress-energy tensor". This new tensor exactly mimicks the electromagnetic stress-energy tensor with Riemann tensor contractions replacing Maxwell tensor contractions. We briefly consider the introduction of matter. A Lagrangian generalizing the two spinor Dirac equations has no gravitational currents and the electromagnetic currents must be on the light cone. A Lagrangian generalizing the Pauli equations has both gravitational and electromagnetic currents. The equations of both Lagrangians demonstrate beautifully how the divergence of the total stress-energy tensor vanishes in this formalism. In the theory of the generalized Einstein-Maxwell and Pauli equations we succeed in deriving an equation describing a generalized matter-charge current density. / Graduate