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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

It is now a consolidated fact that our Universe is undergoing an accelerated expansion. According to Einstein's General Relativity, if the main constituents of our Universe were ordinary and cold dark matter, then we would expect it to be contracting and collapsing due to matter's attractive nature. The simplest explanation we have for this acceleration is in the form of a component with a negative ratio of pressure to density equal to -1 known as cosmological constant, Λ , presently dominating over baryonic and cold dark matter. However, the Λ Cold Dark Matter (Λ CDM) model suffers from a well known fine tuning problem. This led to the formulation of dark energy and modified gravity theories as alternatives to the problem of cosmic acceleration. These theories either include additional degrees of freedom, higher-order equations of motion, extra dimensionalities or imply non-locality. In this thesis we focus on single field scalar tensor theories embedded within Horndeski gravity. Even though there is currently doubt on their ability to explain cosmic acceleration without having a bare cosmological constant on their action, the degree of freedom they introduce mediates an additional fifth force. And while this force has to suppressed on Solar system scales, it can have interesting and observable effects on cosmological scales. Over the next decade there is a surge of surveys that will improve the understanding of our Universe on the largest scales. Hence, in this work, we take several different modified gravity theories and study their impact on cosmological observables. We will analyze the dynamics of linear perturbations on these theories and clearly highlight how they deviate from Λ CDM, allowing to break the degeneracy at the background level. We will also study the evolution of the gravitational potentials on sub horizon scales and provide simplified expressions at this regime and, for some models, obtain constraints using the latest data.

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

Neutron stars are some of the most fascinating objects in Nature. Essentially all aspects of physics seems to be represented inside them. Their cores are likely to contain deconfined quarks, hyperons and other exotic phases of matter in which the strong interaction is the dominant force. The inner region of their solid crust is penetrated by superfluid neutrons and their magnetic fields may reach well over 1012 Gauss. Moreover, their extreme mean densities, well above the densities of nuclei, and their rapid rotation rates makes them truly relativistic both in the special as well as in the general sense. This thesis deals with a small subset of these phenomena. In particular the exciting possibility of trapping of gravita-tional waves is examined from a theoretical point of view. It is shown that the standard condition R < 3M is not essential to the trapping mechanism. This point is illustrated using the elegant tool provided by the optical geometry. It is also shown that a realistic equation of state proposed in the literature allows stable neutron star models with closed circular null orbits, something which is closely related to trapped gravitational waves. Furthermore, the general relativistic theory of elasticity is reviewed and applied to stellar models. Both static equilibrium as well as radially oscillating configurations with elasticsources are examined. Finally, Killing tensors are considered and their applicability to modeling of stars is discussed

<p>We explore a model of dark matter called wave dark matter (also known as scalar field dark matter and boson stars) which has recently been motivated by a new geometric perspective by Bray. Wave dark matter describes dark matter as a scalar field which satisfies the Einstein-Klein-Gordon equations. These equations rely on a fundamental constant Upsilon (also known as the ``mass term'' of the Klein-Gordon equation). Specifically, in this dissertation, we study spherically symmetric wave dark matter and compare these results with observations of dwarf spheroidal galaxies as a first attempt to compare the implications of the theory of wave dark matter with actual observations of dark matter. This includes finding a first estimate of the fundamental constant Upsilon.</p><p>In the introductory Chapter 1, we present some preliminary background material to define and motivate the study of wave dark matter and describe some of the properties of dwarf spheroidal galaxies.</p><p>In Chapter 2, we present several different ways of describing a spherically symmetric spacetime and the resulting metrics. We then focus our discussion on an especially useful form of the metric of a spherically symmetric spacetime in polar-areal coordinates and its properties. In particular, we show how the metric component functions chosen are extremely compatible with notions in Newtonian mechanics. We also show the monotonicity of the Hawking mass in these coordinates. Finally, we discuss how these coordinates and the metric can be used to solve the spherically symmetric Einstein-Klein-Gordon equations.</p><p>In Chapter 3, we explore spherically symmetric solutions to the Einstein-Klein-Gordon equations, the defining equations of wave dark matter, where the scalar field is of the form f(t,r) = exp(i omega t) F(r) for some constant omega in R and complex-valued function F(r). We show that the corresponding metric is static if and only if F(r) = h(r)exp(i a) for some constant a in R and real-valued function h(r). We describe the behavior of the resulting solutions, which are called spherically symmetric static states of wave dark matter. We also describe how, in the low field limit, the parameters defining these static states are related and show that these relationships imply important properties of the static states.</p><p>In Chapter 4, we compare the wave dark matter model to observations to obtain a working value of Upsilon. Specifically, we compare the mass profiles of spherically symmetric static states of wave dark matter to the Burkert mass profiles that have been shown by Salucci et al. to predict well the velocity dispersion profiles of the eight classical dwarf spheroidal galaxies. We show that a reasonable working value for the fundamental constant in the wave dark matter model is Upsilon = 50 yr^(-1). We also show that under precise assumptions the value of Upsilon can be bounded above by 1000 yr^(-1).</p><p>In order to study non-static solutions of the spherically symmetric Einstein-Klein-Gordon equations, we need to be able to evolve these equations through time numerically. Chapter 5 is concerned with presenting the numerical scheme we will use to solve the spherically symmetric Einstein-Klein-Gordon equations in our future work. We will discuss how to appropriately implement the boundary conditions into the scheme as well as some artificial dissipation. We will also discuss the accuracy and stability of the scheme. Finally, we will present some examples that show the scheme in action.</p><p>In Chapter 6, we summarize our results. Finally, Appendix A contains a derivation of the Einstein-Klein-Gordon equations from its corresponding action.</p> / Dissertation

In this thesis, multipole expansions of mass, momentum and stress density will be made for a body in Newtonian mechanics. Using these definitions / momentum, angular momentum, center of mass, force and torque are defined for N gravitationally interacting isolated bodies. Equations of motions of such a system are derived. Definitions of momentum, angular momentum, center of mass, force and torque are made in a relativistic theory. Dynamical (gravitational) skeleton is defined and the multipole moments of the dynamical skeleton are found. Equations of motion for a test body moving in a gravitational field are derived in terms of the multipole moments. Save the details of the derivations, no originality in this thesis is claimed: it is intended as a review of the subject.

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.