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.

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

Philosophiae Doctor - PhD / The matter power spectrum is key to understanding the growth of large-scale structure in the Universe. Upcoming surveys of galaxies in the optical and HI will probe increasingly large scales, approaching and even exceeding the Hubble scale at the survey redshifts. On these cosmological scales, surveys can in principle provide the best constraints on dark energy (DE) and modified gravity models and will be able to test general relativity itself. However, in order to realise the potential of these surveys, we need to ensure that we are using a correct analysis, i.e. a general relativistic analysis, on cosmological scales. There are two fundamental issues underlying the general relativistic (GR) analysis. Firstly, we need to correctly identify the galaxy overdensity that is observed on the past light cone. Secondly, we need to account for all the distortions arising from observing on the past light cone, including redshift distortions (with all general relativistic effects included) and volume distortions. These general elativistic effects appear in the angular power spectra of matter in redshift space. We compute these quantities, taking into account all general relativistic large-scale effects, and including the important contributions from redshift space distortions and lensing convergence. This is done for self-consistent models of DE, known as ‘quintessence’, which have only been very recently treated in the GR approach. Particularly, we focus mainly on computing the predictions (i.e. the power spectra) that need to be confronted with future data. Hence we compute the GR angular power spectra, correcting the 3D Newtonian calculation for several quintessence models. We also compute the observed 3D power spectra for interacting DE (which until now have not previously been studied in the GR approach) – in which dark matter and DE exchange energy and momentum. Interaction in the dark sector can lead to large-scale deviations in the power spectrum, similar to GR effects or modified gravity. For the quintessence case, we found that the DE perturbations make only a small contribution on the largest scales, and a negligible contribution on smaller scales. Ironically, the DE perturbations remove the false boost of large-scale power that arises if we impose the (unphysical) assumption that the DE perturbations vanish. However, for the interacting DE (IDE) case, we found that if relativistic effects are ignored, i.e. if they are not subtracted in order to isolate the IDE effects, the imprint of IDE will be incorrectly identified – which could lead to a bias in constraints on IDE, on horizon scales. Moreover, we found that on super-Hubble scales, GR corrections in the observed galaxy power spectrum are able to distinguish a homogeneous DE (being one whose density perturbation in comoving gauge vanishes) from the concordance model (and from a clustering DE) – at low redshifts and for high magnification bias. Whereas the matter power spectrum is incapable of distinguishing a homogeneous DE from the concordance model. We also found that GR effects become enhanced with decreasing magnification bias, and with increasing redshift.

Techniques for numerically constructing initial data in the 3+1 formalism of general relativity (GR) are studied, using the theoretical framework described in Bowen and York (1980), Physical Review D 21(8), 2047-2056. The two main assumptions made are maximal slicing and 3-conformal flatness of the generated spaces. For ease of numerical solution, axisymmetry is also assumed, but all the results should extend without difficulty to the non-axisymmetric case. The numerical code described in this thesis may be used to construct vacuum spaces containing arbitrary numbers of black holes, each with freely specifyable (subject to the axisymmetry assumption) position, mass, linear momentum, and angular momentum. It should be emphasised that the time evolution of these spaces has not yet been attempted. There are two significant innovations in this work: the use of a new boundary condition for the surfaces of the black holes, and the use of multiple coordinate patches in the numerical solution. The new boundary condition studied herein requires the inner boundary of the numerical grid to be a marginally trapped surface. This is in contrast to the approach used in much previous work on this problem area, which requires the constructed spaces to be conformally isometric under a "reflection mapping" which interchanges the interior of a specified black hole with the remainder of the space. The new boundary condition is found to be easy to implement, even for multiple black holes. It may also prove useful in time evolution problems. The coordinate choice scheme introduced in this thesis uses multiple coordinate patches in the numerical solution, each with a coordinate system suited to the local physical symmetries of the region of space it covers. Because each patch need only cover part of the space, the metrics on the individual patches can be kept simple, while the overall patch system still covers a complicated topology. The patches are linked together by interpolation across the interpatch boundaries. Bilinear interpolation suffices to give accuracy comparable with that of common second order difference schemes used in numerical GR. This use of multiple coordinate patches is found to work very well in both one and two black hole models, and should generalise to a wide variety of other numerical GR problems. Patches are also found to be a useful (if somewhat over-general) way of introducing spatially varying grid sizes into the numerical code. However, problems may arise when trying to use multiple patches in time evolution problems, in that the interpatch boundaries must not become spurious generators or reflectors of gravitational radiation, due to the interpolation errors. These problems have not yet been studied. The code described in this thesis is tested against Schwarzschild models and against previously published work using the Bowen and York formalism, reproducing the latter within the limits of error of the codes involved. A number of new spaces containing one and two black holes with linear or angular momentum are also constructed to demonstrate the code, although little analysis of these spaces has yet been done. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

No description available.

One of the most fundamental problems in classical general relativity is the measure of e↵ective mass of a pure gravitational field. The principle of equivalence prohibits a purely local measure of this mass. This thesis critically examines the most recent quasi-local measure by Wang and Yau for a maximally rotating black hole spacetime. In particular, it examines a family of spacelike 2-surfaces with constant radii in Boyer-Lindquist coordinates. There exists a critical radius r* below which, the Wang and Yau quasi-local energy has yet to be explored. In this region, the results of this thesis indicate that the Wang and Yau quasi-local energy yields complex values and is essentially equivalent to the previously defined Brown and York quasi-local energy. However, an application of their quasi-local mass is suggested in a dynamical setting, which can potentially give new and meaningful measures. In supporting this thesis, the development of a novel adiabatic isometric mapping algorithm is included. Its purpose is to provide the isometric embedding of convex 2-surfaces with spherical topology into Euclidean 3-space necessary for completing the calculation of quasilocal energy in numerical relativity codes. The innovation of this algorithm is the guided adiabatic pull- back routine. This uses Ricci flow and Newtons method to give isometric embeddings of piecewise simplicial 2-manifolds, which allows the algorithm to provide accuracy of the edge lengths up to a user set tolerance. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2017. / FAU Electronic Theses and Dissertations Collection

Thesis (Ph. D.)--University of Chicago, Dept. of Physics, June 1999. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 106-111). Also available on the Internet.

Thesis (Ph. D.)--University of Chicago, Dept. of Physics, 2002. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 106-111). Also available on the Internet.