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

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In the generation of the standard GRACE gravity fields, the K-Band Ranging (KBR) system data is used in its range-rate mode. Because time derivatives attenuate the gravity signal relative to the data noise at the lower frequencies, it is thought that solutions using range data might have better low-degree (low-frequency) characteristics. The purpose of this work is to detail the methods required to generate range-based solutions, to determine some of the properties of these solutions and then to compare them to range-rate based solutions. It is demonstrated that the range-based solutions are feasible. Different subarc lengths and parameterizations were considered. Although, the most effective combination of subarc lengths and parameterizations are not picked, it is concluded that estimating the mixed periodic term along with bias, bias-rate, bias-acceleration and periodic terms degrades the quality of the range based solution and therefore should not be used. Further study is necessary to pick the optimal combination of subarc length and parameterization which would be used in the time-series analysis. / text

In this dissertation we study radiating stars in strong gravitational elds. We generate new classes of exact solutions to the Einstein eld equations and the boundary condition applicable to radiating relativistic stars. The model of a radiating star in general relativity, matching to the Vaidya exterior spacetime, is reviewed. The boundary condition is converted to a Riccati equation and we consider both cases involving geodesic and non-geodesic particle trajectories. We present the metrics found previously. We rst solve the boundary condition for the geodesic case and nd the gravitational potentials which are expanding and shearing. This is a new result. Secondly the boundary condition is analysed for the non-geodesic case and we seek new gravitational potentials which are accelerating, expanding and shearing. We are able to identify only geodesic solutions for this second case; this appears to be a new class of models. The solutions found are presented in terms of elementary functions which are helpful in studying the physical properties. The new solutions found cannot be categorised in existing classes of known solutions; they are examples of a new generic class di erent from previous studies. The matter variables of the model are generated . / Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2012.

Thesis (Ph. D.)--University of Texas at Austin, 2003. / Supervisors: Philip J. Morrison and Matthew W. Choptuik. Vita. Includes bibliographical references. Also available from UMI.

In this work, we develop effective field theory (EFT) methods for the study of a wide variety of condensed matter systems, including superfluids, ordinary fluids, solids, and supersolids. As a first application, we focus on the dynamics of vortex lines in trapped superfluid condensates, studying their precessional motion and working out the frequency of precession from EFT principles. We consider the effects of trapping in two and three dimensions, as well as implications of trapping for the dispersion relation of Kelvin waves along superfluid vortex lines. We also apply our formalism to study the effects of gravitational fields on sound waves in several different media, discovering that localized sound waves propagate with an associated (negative) net mass, which in turn generates a tiny gravitational field. We confirm that this effect is a robust result that can be found from purely classical, non-relativistic methods. We then present three Lorentz invariant, renormalizable, weakly coupled theories that implement the symmetry-breaking pattern of a perturbative homogeneous and isotropic solid, as potential UV-completions of the low-energy effective theory that we studied. We demonstrate that a particular class of homogeneous, isotropic solids at long distances corresponds to states that are also homogeneous at short distances, unlike typical solids found in nature. We find that each case leads to the same rather unorthodox effective theory of a solid with luminal transverse excitations. Finally, we discuss applications of the methods we have developed and the potential for interesting new directions of this research.

This thesis concerns the use of observations of gravitational waves as tools for astronomy and fundamental physics. Gravitational waves are small ripples in spacetime produced by rapidly accelerating masses; their existence has been predicted for almost 100 years, but the first direct evidence of their existence came only very recently with the announcement in February 2016 of the detection by the LIGO and VIRGO collaborations. Part I of this thesis presents an introduction to gravitational wave astronomy, including a detailed discussion of a wide range of gravitational wave sources, their signal morphologies, and the experimental detectors used to observe them. Part II of this thesis concerns a particular data analysis problem which often arises when trying to infer the source properties from a gravitational wave observation. The use of an inaccurate signal model can cause significant systematic errors in the inferred source parameters. The work in this section concerns a proposed technique, called the Gaussian process marginalised likelihood, for overcoming this problem. Part III of this thesis concerns the possibility of testing if the gravitational field around an astrophysical black hole conforms to the predictions of general relativity and the cosmic censorship hypothesis. It is expected that the gravitational field should be well described by the famous Kerr solution. Two approaches for testing this hypothesis are considered; one using X-ray observations and one using gravitational waves. The results from these two approaches are compared and contrasted. Finally, the conclusions and a discussion of future prospects are presented in part IV of this thesis.

We study several different models of extended bodies in gravitational fields. Firstly, we revisit the glider model of a dumbbell-like oscillating body. We develop an independent scheme to integrate the equations of motion. We study the radial fall of a Newtonian spring, calculate the position shifts of the spring and find the critical value of the spring constant which cannot overcome the tidal forces. We argue that the relativistic glider model is unphysical due to its behaviour in the critical regions. Secondly, we show that Dixon's theory of extended bodies predicts a geodesic motion of the centre of mass in maximally symmetric spacetimes. We prove that a system of test particles can be described by a conserved stress-energy tensor and we evaluate the position shifts of the glider model in the maximally symmetric spacetimes, showing its disagreement with Dixon's theory. We thus conclude again that the glider model must be rejected. And thirdly, we study a model of an extended body consisting of interacting particles, which is in accord with Dixon's theory. We calculate the position shifts for this model and show that the model does not predict any measurable swimming effect. Finally, we estimate the numerical error of the calculation by finding the position shifts of the model in maximally symmetric...

Orientador: Eugenio Spano Rosa / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-07-25T04:17:15Z (GMT). No. of bitstreams: 1 Morandin_MarceloLuiz_M.pdf: 6899296 bytes, checksum: 3abf17e0fd6016b0fea94b6bccdb6487 (MD5) Previous issue date: 1999 / Resumo: O estudo desenvolvido têm como tema central separadores cic1ônicos gás-líquido. Mais precisamente, procura-se caracterizar experimentalmente e desenvolver um modelo que possa prever o comportamento do escoamento de líquido que se desenvolve na forma de um filme de espessura reduzida sob a ação combinada dos campos centrífugo e gravitacional de forças, sendo esta uma das principais características dos separadores ciclônicos. Para tal, utiliza-se de duas técnicas experimentais para determinação direta da espessura média do filme de líquido: sonda de condutância e ultra-som. Por meio de visualização o ângulo que o filme faz com a horizontal também é determinado experimentalmente. Uma combinação destas variáveis experimentais permite uma determinação indireta das componentes axial e tangencial da velocidade média local do filme. Um modelo é desenvolvido a partir das equações de camada limite na forma integral tomada em termos médios num sistema cilíndrico de coordenadas e sob a hipótese de escoamento axisimétrico. São realizadas comparações entre as técnicas experimentais empregadas e os dados utilizados para validar o modelo proposto / Abstract: The work is applied to the gas-liquid separator field and focus on the hydrodynamics aspects of the developing liquid film under the action of centrifugal and gravitational force fields. The main objective is to characterize experimentally the liquid film and develop a model capable to predict the average film quantities. Toward this objective two experimental techniques are employed to measure the average film thickness distribution: a conductive probe and ultrasound. AIso, using flow visualization the angle of the film with respect to the horizontal is determined. Using these two experimentally variable and the mass flow rate, the axial and tangentiallocal average film velocity is indirectly achieved. The flow modei developed is based on the integral form of the boundary layer equations in a cylindrical coordinate system and assuming axis-symmetric flow. A direct comparison between the film thickness experimental techniques is drawn as well as the model validation is conducted against the experimental data / Mestrado / Fenomenos de Transporte / Mestre em Engenharia Mecânica

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