According the linguistic relativity hypothesis, the language one speaks affects how one thinks. Because languages differ in how they categorize color, linguistic relativity has often been tested by conducting experiments on color perception and memory. This study examines the linguistic relativity hypothesis using ecologically valid stimuli: pictures of eyes. Because Russian-speakers are more likely to describe blue/grey eyes as grey, whereas English speakers are more likely to describe them as blue, English and Russian participants were asked to match the overall color of blue eyes to a color scale. There were three conditions. In the first condition (perception), participants saw the color scale and an eye picture simultaneously and then chose the color that best matched the picture. In the second condition (memory), participants matched the color of an eye to the color scale from memory. The third condition (label) was similar to the second, except participants labeled the eye orally before matching the color from memory. A 3 (condition) x 2 (language) ANCOVA and Bayesian analysis were used to analyze the data. Overall, the ANCOVA and Bayesian analysis indicated that there was a main effect of language. Russian-speaking participants were more likely to rate the eyes as greyer than English-speaking participants. The Bayesian analysis also suggested that there may also have been an interaction, with Russian and English-speaking participants rating the eyes similarly in the perception condition, but not the memory or labeling conditions. Overall, the findings provide novel evidence for the linguistic relativity hypothesis.

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

This thesis is a study of the validity and application of the on-shell recursion relations within the theory of General Relativity. These relations are also known as the Britto-Cachazo-Feng-Witten (BCFW) relations. They reduce the calculation of a tree-level graviton scattering amplitude into the evaluation of two smaller physical amplitudes and of a propagator. With multiple applications of the recursion relations, amplitudes can be uniquely constructed from fundamental three-graviton amplitudes. The BCFW prescriptions were first applied to gauge theory. We thus provide a self-contained description of their usage in this context. We then generalize the proof of their validity to include gravity. The BCFW recursion relations can then be used to reconstruct the full theory from cubic vertices. We finally describe how these three-graviton vertices can be determined uniquely from Poincare symmetries.

This dissertation describes a multidimensional relativistic hydrodynamic code which solves the special relativistic hydrodynamic equations as a hyperbolic system of conservation laws based on the total variation diminishing (TVD) scheme. Several standard tests and test simulations are presented to demonstrate the accuracy, robustness and flexibility of the code. Using this code we have studied three-dimensional hydrodynamic interactions of relativistic extragalactic jets with two-phase ambient media. The deflection angle of the jet is influenced more by the density contrast of the cloud than by the beam Mach number of the jet, and a relativistic jet with low relativistic beam Mach number can eventually be slightly bent after it crosses the dense cloud. Relativistic jet impacts on dense clouds do not necessarily destroy the clouds completely, and much of the cloud body can survive as a coherent blob due to the combination of the geometric influence of off-axis collisions and the lower rate of cloud fragmentation through the Kelvin-Helmholtz instability for relativistic flows. We find that relativistic jets interacting with clouds can produce synchrotron emission knots similar to structures observed in many VLBI-scale radio sources and the synchrotron emission peaks right before the jet passes through the cloud.

This thesis is a study of the validity and application of the on-shell recursion relations within the theory of General Relativity. These relations are also known as the Britto-Cachazo-Feng-Witten (BCFW) relations. They reduce the calculation of a tree-level graviton scattering amplitude into the evaluation of two smaller physical amplitudes and of a propagator. With multiple applications of the recursion relations, amplitudes can be uniquely constructed from fundamental three-graviton amplitudes. The BCFW prescriptions were first applied to gauge theory. We thus provide a self-contained description of their usage in this context. We then generalize the proof of their validity to include gravity. The BCFW recursion relations can then be used to reconstruct the full theory from cubic vertices. We finally describe how these three-graviton vertices can be determined uniquely from Poincare symmetries.

<p>In general relativity, the Riemannian Penrose inequality (RPI) provides a lower bound for the ADM mass of an asymptotically flat manifold of nonnegative scalar curvature in terms of the area of the outermost minimal surface, if one exists. In physical terms, an equivalent statement is that the total mass of an asymptotically flat spacetime admitting a time-symmetric spacelike slice is at least the mass of any black holes that are present, assuming nonnegative energy density. The main goal of this thesis is to deduce geometric lower bounds for the ADM mass of manifolds to which neither the RPI nor the famous positive mass theorem (PMT) apply. This is the case, for instance, for manifolds that contain metric singularities or have boundary components that are not minimal surfaces.</p> <p>The fundamental technique is the use of conformal deformations of a given Riemannian metric to arrive at a new Riemannian manifold to which either the PMT or RPI applies. Along the way we are led to consider the geometry of certain types non-smooth metrics. We prove a result regarding the local structure of area-minimizing hypersurfaces with respect such metrics using geometric measure theory.</p> <p>One application is to the theory of ``zero area singularities,'' a type of singularity that generalizes the degenerate behavior of the Schwarzschild metric of negative mass. Another application deals with constructing and understanding some new invariants of the harmonic conformal class of an asymptotically flat metric.</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.

The purpose of this thesis is to develop a critical reading of Badiou&rsquo / s theory of truth. Contemporary popular trends such as postmodernism and anti-philosophy champion the principles of pluralism and contingency. They use these against Hegel&rsquo / s conception of history and theory of &lsquo / relational totality&rsquo / . Badiou agrees with these trends. But he criticizes their relativist theory of truth. He wants to provide an &lsquo / objective&rsquo / foundation for &lsquo / truth&rsquo / . The question I wish to explore in this thesis is then to analyze critically Badiou&rsquo / s work to find out whether he succeeds? To do this I am presenting Badiou&rsquo / s philosophical sources in ancient and modern philosophy and his main concepts he relies on. I am analyzing in particular in depth Badiou&rsquo / s understanding of ontology and phenomenology. To explain his concept of truth, I am analyzing his concepts of &lsquo / void&rsquo / , &lsquo / plurality&rsquo / , &lsquo / infinity&rsquo / . However, to make sense of his theory of truth more fully, I am looking also at his conceptions of &lsquo / event&rsquo / and subject&rsquo / , which are the main components of his theory of truth. After having analyzed his theory of of truth, I am looking at his conception of emancipatory politics, to see how his conception of truth works in his practical philosophy.