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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
161

On gravitational wave modeling: numerical relativity data analysis, the excitation of kerr quasinormal modes, and the unsupervised machine learning of waveform morphology

London, Lionel 21 September 2015 (has links)
The expectation that light waves are the only way to gather information about the distant universe dominated scientific thought, without serious alternative, until Einstein’s 1916 proposal that gravitational waves are generated by the dynamics of massive objects. Now, after nearly a century of speculation, theoretical development, observational support, and finally, tremendous experimental preparation, there are good reasons to believe that we will soon directly detect gravitational waves. One of the most important of these good reasons is the fact that matched filtering enables us to dig gravitational wave signals out of noisy data, if we have prior information about the signal’s morphology. Thus, at the interface of Numerical Relativity simulation, and data analysis for experiment, there is a central effort to model likely gravitational wave signals. In this context, I present my contributions to the modeling of Gravitational Ringdown (Kerr Quasinormal Modes). Specifically by ap- propriately interfacing black hole perturbation theory with Numerical Relativity, I present the first robust models for Quasinormal Mode excitation. I present the first systematic de- scription of Quasinormal Mode overtones in simulated binary black hole mergers. I present the first systematic description of nonlinear Quasinormal Mode excitation in simulated bi- nary black hole mergers. Lastly, it is suggested that by analyzing the phase of black hole Quasinormal Modes, we may learn information about the black hole’s motion with respect to the line of sight. Moreover, I present ongoing work at the intersection of gravitational wave modeling and machine learning. This work shows promise for the automated and near optimal placement of Numerical Relativity simulations concurrent with the near optimal linear modeling of gravitational output.
162

Cosmological Models and Singularities in General Relativity

Sandin, Patrik January 2011 (has links)
This is a thesis on general relativity. It analyzes dynamical properties of Einstein's field equations in cosmology and in the vicinity of spacetime singularities in a number of different situations. Different techniques are used depending on the particular problem under study; dynamical systems methods are applied to cosmological models with spatial homogeneity; Hamiltonian methods are used in connection with dynamical systems to find global monotone quantities determining the asymptotic states; Fuchsian methods are used to quantify the structure of singularities in spacetimes without symmetries. All these separate methods of analysis provide insights about different facets of the structure of the equations, while at the same time they show the relationships between those facets when the different methods are used to analyze overlapping areas. The thesis consists of two parts. Part I reviews the areas of mathematics and cosmology necessary to understand the material in part II, which consists of five papers. The first two of those papers uses dynamical systems methods to analyze the simplest possible homogeneous model with two tilted perfect fluids with a linear equation of state. The third paper investigates the past asymptotic dynamics of barotropic multi-fluid models that approach a `silent and local' space-like singularity to the past. The fourth paper uses Hamiltonian methods to derive new monotone functions for the tilted Bianchi type II model that can be used to completely characterize the future asymptotic states globally. The last paper proves that there exists a full set of solutions to Einstein's field equations coupled to an ultra-stiff perfect fluid that has an initial singularity that is very much like the singularity in Friedman models in a precisely defined way. / <p>Status of the paper "Perfect Fluids and Generic Spacelike Singularities" has changed from manuscript to published since the thesis defense.</p>
163

Integrable Nonlinear Relativistic Equations

Hadad, Yaron January 2013 (has links)
This work focuses on three nonlinear relativistic equations: the symmetric Chiral field equation, Einstein's field equation for metrics with two commuting Killing vectors and Einstein's field equation for diagonal metrics that depend on three variables. The symmetric Chiral field equation is studied using the Zakharov-Mikhailov transform, with which its infinitely many local conservation laws are derived and its solitons on diagonal backgrounds are studied. It is also proven that it is equivalent to a novel equation that poses a fascinating similarity to the Sinh-Gordon equation. For the 1+1 Einstein equation the Belinski-Zakharov transformation is explored. It is used to derive explicit formula for N gravitational solitons on arbitrary diagonal background. In particular, the method is used to derive gravitational solitons on the Einstein-Rosen background. The similarities and differences between the attributes of the solitons of the symmetric Chiral field equation and those of the 1+1 Einstein equation are emphasized, and their origin is pointed out. For the 1+2 Einstein equation, new equations describing diagonal metrics are derived and their compatibility is proven. Different gravitational waves are studied that naturally extend the class of Bondi-Pirani-Robinson waves. It is further shown that the Bondi-Pirani-Robinson waves are stable with respect to perturbations of the spacetime. Their stability is closely related to the stability of the Schwarzschild black hole and the relation between the two allows to conjecture about the stability of a wide range of gravitational phenomena. Lastly, a new set of equations that describe weak gravitational waves is derived. This new system of equations is closely and fundamentally connected with the nonlinear Schrödinger equation and can be properly called the nonlinear Schrödinger-Einstein equations. A few preliminary solutions are constructed.
164

Radiating solutions with heat flow in general relativity.

Govender, Megandren. January 1994 (has links)
In this thesis we model spherically symmetric radiating stars dissipating energy in the form of a radial heat flux. We assume that the spacetime for the interior matter distribution is shear-free. The junction conditions necessary for the matching of the exterior Vaidya solution to an interior radiating line element are obtained. In particular we show that the pressure at the boundary of the star is nonvanishing when the star is radiating (Santos 1985). The junction conditions, with a nonvanishing cosmological constant, were obtained. This generalises the results of Santos (1985) and we believe that this is an original result. The Kramer (1992) model is reviewed in detail and extended. The evolution of this model depends on a function of time which has to satisfy a nonlinear second order differential equation. We solve this differential equation in general and thereby completely describe the temporal behaviour of the Kramer model. Graphical representations of the thermodynamical and gravitational variables are generated with the aid of the software package MATHEMATICA Version 2.0 (Wolfram 1991). We also analyse two other techniques to generate exact solutions to the Einstein field equations for modelling radiating stars. In the first case the particle trajectories are assumed to be geodesics. We indicate how the model of Kolassis et al (1988) may be extended by providing an ansatz to solve a second order differential equation. In the second case we review the models of de Oliveira et al (1985, 1986, 1988) where the gravitational potentials are separable functions of the spatial and temporal coordinates. / Thesis (M.Sc.)-University of Natal, 1994.
165

Volume-Preserving Coordinate Gauges in Linear Perturbation Theory

Herman, David Leigh 21 December 2012 (has links)
The main goal of this thesis is to present cosmological perturbation theory (based on the standard Friedmann cosmological model) in volume-preserving coordinates, which then provides a suitable basis for studies in cosmological averaging. We review perturbation theory to second order, allowing for averaging to second order in future research. To solve the averaging problem we need a method of covariantly and gauge invariantly averaging tensorial objects on a background manifold. This is a very difficult problem. However, the definition of an average takes on a particularly simple form when written in a system of volume-preserving coordinates. Therefore, we develop a three dimensional and a four dimensional volume-preserving coordinate gauge in this thesis that can be used for averaging in cosmological perturbation theory.
166

Degenerate Kundt Spacetimes and the Equivalence Problem

McNutt, David 20 March 2013 (has links)
This thesis is mainly focused on the equivalence problem for a subclass of Lorentzian manifolds: the degenerate Kundt spacetimes. These spacetimes are not defined uniquely by their scalar curvature invariants. To prove two metrics are diffeomorphic, one must apply Cartan's equivalence algorithm, which is a non-trivial task: in four dimensions Karlhede has adapted the algorithm to the formalism of General Relativity and significant effort has been spent applying this algorithm to particular subcases. No work has been done on the higher dimensional case. First, we study the existence of a non-spacelike symmetry in two well-known subclasses of the N dimensional degenerate Kundt spacetimes: those spacetimes with constant scalar curvature invariants (CSI) and those admitting a covariant constant null vector (CCNV). We classify the CSI and CCNV spacetimes in terms of the form of the Killing vector giving constraints for the metric functions in each case. For the rest of the thesis we fix N=4 and study a subclass of the CSI spacetimes: the CSI-? spacetimes, in which all scalar curvature invariants vanish except those constructed from the cosmological constant. We produce an invariant characterization of all CSI-? spacetimes. The Petrov type N solutions have been classified using two scalar invariants. However, this classification is incomplete: given two plane-fronted gravitational waves in which both pairs of invariants are similar, one cannot prove the two metrics are equivalent. Even in this relatively simple subclass, the Karlhede algorithm is non-trivial to implement. We apply the Karlhede algorithm to the collection of vacuum Type N VSI (CSI-?, ? = 0) spacetimes consisting of the vacuum PP-wave and vacuum Kundt wave spacetimes. We show that the upper-bound needed to classify any Type N vacuum VSI metric is four. In the case of the vacuum PP-waves we have proven that the upper-bound is sharp, while in the case of the Kundt waves we have lowered the upper-bound from five to four. We also produce a suite of invariants that characterize each set of non-equivalent metrics in this collection. As an application we show how these invariants may be related to the physical interpretation of the vacuum plane wave spacetimes.
167

Spherically symmetric cosmological solutions.

Govender, Jagathesan. January 1996 (has links)
This thesis examines the role of shear in inhomogeneous spherically symmetric spacetimes in the field of general relativity. The Einstein field equations are derived for a perfect fluid source in comoving coordinates. By assuming a barotropic equation of state, two classes of nonaccelerating solutions are obtained for the Einstein field equations. The first class has equation of state p = ⅓µ and the second class, with equation of state p = µ, generalises the models of Van den Bergh and Wils (1985). For a particular choice of a metric potential a new class of solutions is found which is expressible in terms of elliptic functions of the first and third kind in general. A class of nonexpanding cosmological models is briefly studied. The method of Lie symmetries of differential equations generates a self-similar variable which reduces the field and conservation equations to a system of ordinary differential equations. The behaviour of the gravitational field in this case is governed by a Riccati equation which is solved in general. Another class of solutions is obtained by making an ad hoc choice for one of the gravitational potentials. It is demonstrated that for a stiff fluid a particular case of the generalised Emden-Fowler equation arises. / Thesis (Ph.D.)-University of Natal, Durban, 1996.
168

Conformally invariant relativistic solutions.

Maharaj, M. S. January 1993 (has links)
The study of exact solutions to the Einstein and Einstein-Maxwell field equations, by imposing a symmetry requirement on the manifold, has been the subject of much recent research. In this thesis we consider specifically conformal symmetries in static and nonstatic spherically symmetric spacetimes. We find conformally invariant solutions, for spherically symmetric vectors, to the Einstein-Maxwell field equations for static spacetimes. These solutions generalise results found previously and have the advantage of being regular in the interior of the sphere. The general solution to the conformal Killing vector equation for static spherically symmetric spacetimes is found. This solution is subject to integrability conditions that place restrictions on the metric functions. From the general solution we regain the special cases of Killing vectors, homothetic vectors and spherically symmetric vectors with a static conformal factor. Inheriting conformal vectors in static spacetimes are also identified. We find a new class of accelerating, expanding and shearing cosmological solutions in nonstatic spherically symmetric spacetimes. These solutions satisfy an equation of state which is a generalisation of the stiff equation of state. We also show that this solution admits a conformal Killing vector which is explicitly obtained. / Thesis (Ph.D.)-University of Natal, Durban, 1993.
169

Conformal motions in Bianchi I spacetime.

Lortan, Darren Brendan. January 1992 (has links)
In this thesis we study the physical properties of the manifold in general relativity that admits a conformal motion. The results obtained are general as the metric tensor field is not specified. We obtain the Lie derivative along a conformal Killing vector of the kinematical and dynamical quantities for the general energy-momentum tensor of neutral matter. Equations obtained previously are regained as special cases from our results. We also find the Lie derivative of the energy-momentum tensor for the electromagnetic field. In particular we comprehensively study conformal symmetries in the Bianchi I spacetime. The conformal Killing vector equation is integrated to obtain the general conformal Killing vector and the conformal factor subject to integrability conditions. These conditions place restrictions on the metric functions. A particular solution is exhibited which demonstrates that these conditions have a nonempty solution set. The solution obtained is a generalisation of the results of Moodley (1991) who considered locally rotationally symmetric spacetimes. The Killing vectors are regained as special cases of the conformal solution. There do not exist any proper special conformal Killing vectors in the Bianchi I spacetime. The homothetic vector is found for a nonvanishing constant conformal factor. We establish that the vacuum Kasner solution is the only Bianchi I spacetime that admits a homothetic vector. Furthermore we isolate a class of vectors from the solution which causes the Bianchi I model to degenerate into a spacetime of higher symmetry. / Thesis (M.Sc.)-University of KwaZulu-Natal, 1992.
170

On Stephani universes.

Moopanar, Selvandren. January 1992 (has links)
In this dissertation we study conformal symmetries in the Stephani universe which is a generalisation of the Robertson-Walker models. The kinematics and dynamics of the Stephani universe are discussed. The conformal Killing vector equation for the Stephani metric is integrated to obtain the general solution subject to integrability conditions that restrict the metric functions. Explicit forms are obtained for the conformal Killing vector as well as the conformal factor . There are three categories of solution. The solution may be categorized in terms of the metric functions k and R. As the case kR - kR = 0 is the most complicated, we provide all the details of the integration procedure. We write the solution in compact vector notation. As the case k = 0 is simple, we only state the solution without any details. In this case we exhibit a conformal Killing vector normal to hypersurfaces t = constant which is an analogue of a vector in the k = 0 Robertson-Walker spacetimes. The above two cases contain the conformal Killing vectors of Robertson-Walker spacetimes. For the last case in - kR = 0, k =I 0 we provide an outline of the integration process. This case gives conformal Killing vectors which do not reduce to those of RobertsonWalker spacetimes. A number of the calculations performed in finding the solution of the conformal Killing vector equation are extremely difficult to analyse by hand. We therefore utilise the symbolic manipulation capabilities of Mathematica (Ver 2.0) (Wolfram 1991) to assist with calculations. / Thesis (M.Sc.)-University of Natal, Durban, 1992.

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