It has long been presumed that any consistent nonlinear theory of a spin-two field must be generally covariant. Using Wald's consistency criteria, we exhibit classes of nonlinear theories of a spin-two field that do not have general covariance. We consider four alternative formulations of the spin-two equations. As a first example, we consider a conformally invariant theory of a spin-two field coupled to a scalar field. In the next two cases, the usual symmetric rank-two tensor field, γab, is chosen as the potential. In the fourth case, a traceless symmetric rank-two tensor field is used as the potential. We find that consistent nonlinear generalization of these different formulations leads to theories of a spin-two field that are not generally covariant. In particular, we find types of theories which, when interpreted in terms of a metric, are invariant under the infinitesimal gauge transformation γab→γab + ∇ (a∇[symbol omitted]K[symbol omitted]), where Kab is an arbitrary two-form field. In addition, we find classes of theories that are conformally invariant. As a related problem, we compare the types of theories obtained from the nonlinear extension of a divergence- and curl-free vector field when it is described in terms of two of its equivalent formulations. We find that nonlinear extension of the theory is quite different in each case. Moreover, the resulting types of nonlinear theories may not necessarily be equivalent. A similar analysis is carried out for three-dimensional electromagnetism. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

published_or_final_version / Physics / Doctoral / Doctor of Philosophy

We employ a stochastic approach that models spacetime fluctuations close to the Planck scale by means of a classical, randomly fluctuating metric (random gravity framework).  We enrich the classical scheme for metric perturbations over a curved background by also including matter fields and metric conformal fluctuations.  We show in general that a conformally modulated metric induces dephasing as a result of an effective nonlinear Newtonian potential obtained in the appropriate non-relativistic limit of a minimally coupled Klein-Gordon field.  The special case of vacuum fluctuations is considered and a quantitative estimate of the expected effect deduced. Secondly, we address the question of how conformal fluctuations could physically arise.  By applying the random gravity framework we first show that standard GR seems to forbid spontaneous conformal metric modulations.  Finally we argue that a different result follows within scalar-tensor theories of gravity such as e.g. Brans-Dicke theory. In this case a conformal modulation of the metric arises naturally as a result of the fluctuations in the Brans-Dicke field and quantum dephasing of a test particle is expected to occur.  For large negative values of the coupling parameter the conformal fluctuations may also contribute to alleviate the well known problem of the large zero point energy due to quantum matter fields.

Chan Kin Hang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 66-67). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Weighted Sobolev Spaces --- p.3 / Chapter 2.1 --- Weighted Sobolev Spaces --- p.3 / Chapter 2.2 --- Some Basic Properties of Weighted Sobolev Spaces --- p.4 / Chapter 2.3 --- Δon Rn in Weighted Sobolev Spaces --- p.14 / Chapter 2.4 --- Δg on Asymptotically Flat Manifolds --- p.20 / Chapter 3 --- Uniqueness of Structure at Infinity --- p.32 / Chapter 3.1 --- More on Δg --- p.32 / Chapter 3.2 --- Uniqueness of Structure of Infinity --- p.34 / Chapter 4 --- Uniqueness of Mass --- p.40 / Chapter 4.1 --- Definition of Mass --- p.40 / Chapter 4.2 --- Uniqueness of Mass --- p.41 / Chapter 5 --- Schwarzschild Metric and Vacuum Einstein Equation --- p.50 / Chapter 5.1 --- Static Spacetime and Spherically Symmetric Spacetime --- p.50 / Chapter 5.2 --- Schwarzschild Vacuum Solution --- p.57 / Chapter 5.2.1 --- Equation Solving --- p.57 / Chapter 5.3 --- Birkhoff's Theorem --- p.59 / Chapter 5.4 --- Asymptotically Flat Properties of Space with Schwarzschild Metric --- p.61 / Chapter 5.5 --- Mass of The Space Induced by Schwarzschild Metric --- p.64 / Bibliography --- p.66

published_or_final_version / Physics / Master / Master of Philosophy

No description available.

In this thesis we seek exact solutions to the isotropic Einstien-Maxwell system that model the interior of relativistic stars. The field equations are transformed to a simpler form using the transformation of Durgapal and Bannerji (1983); the integration of the system is reduced to solving the condition of pressure isotropy. This condition is a recurrence relation with variable rational coe±cients which can be solved in general. New classes of solutions of linearly independent functions are obtained in terms of special functions and elementary functions for different spatial geometries. Our results contain models found previously including the superdense Tikekar (1990) neutron star model, the uncharged isotropic Maharaj and Leach (1996) solutions, the Finch and Skea (1989) model and the Durgapal and Bannerji (1983) superdense neutron star. Our general class of solutions also contain charged relativistic spheres found previously, including the model of Hansraj and Maharaj (2006) and the model of Thirukkanesh and Maharaj (2006). In addition, two exact analytical solutions describing the interior of a charged strange quark star are obtained by applying the MIT bag equation of state. We regain the Mak and Harko (2004) solution for a charged quark star as a special case. / Thesis (Ph. D.) University of KwaZulu-Natal, Westville, 2007.

In this thesis we study the conformal symmetries in two locally rotationally symmetric spacetimes and the homothetic symmetries of a Bianchi I spacetime. The conformal Killing equation in a class AIa spacetime (MacCallum 1980), with a G4 of motions, is integrated to obtain the general solution subject to integrability conditions. These conditions are comprehensively analysed to determine the restrictions on the metric functions. The Killing vectors are contained in the general conformal solution. The homothetic vector is obtained and the explicit functional dependence of the metric functions determined. The class AIa spacetime does not admit a nontrivial special conformal factor. We also integrate the conformal Killing equation in the anisotropic locally rotationally symmetric spacetime of class A3 (MacCallum 1980), with a G4 of motions, to obtain the general conformal Killing vector and the conformal factor subject to integrability conditions. The Killing vectors are obtained as a special case from the general conformal solution. The homothetic vector is found for a nonzero constant conformal factor. The explicit functional form of the metric functions is determined for the existence of this homothetic vector. The spatially homogeneous and anisotropic A3 spacetime also does not admit a nontrivial special conformal vector. In the Bianchi I spacetime, with a G3 of motions, the conformal Killing equation is integrated for a constant conformal factor to generate the homothetic symmetries. The integrability conditions are solved to determine the functional dependence of the three time-dependent metric functions. / Thesis (M.Sc.)-University of Natal, Durban, 1991.

Thesis (Ph. D.)--University of Hong Kong, 1998. / Includes bibliographical references.

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