Aspects of a spherically symmetric model of the post-decoupling universe

Bibliography: pages 84-88.The central aim of this thesis is to consider aspects of the spherically symmetric Lemaitre-Tolman-Bondi (LTB) solution as a model of the post-decoupling universe. To do this comprehensively is a massive task and is not our aim here. Indeed, far from it, we will concentrate on select instances of this programme and attempt in some places to indicate possibilities for further study. There are many solutions of the EFE which satisfy what we consider to be 'reasonable criteria' for a cosmology and others that do not. The LTB solution may be accepted as a reasonable cosmological model because ■ It allows non-empty solutions. ■ It allows expanding solutions. ■ It has a homogeneous and isotropic limit. ■ It allows for inhomogeneity

Dynamical studies in relativistic cosmology

Bibliography: leaves 158-167.We conduct three investigations in Relativistic Cosmology that is the Einstein Field Equations applied to the largest scales with source field typically taken to be a perfect fluid and fundamental observers comoving with the preferred fluid four-velocity. We show using a tetrad analysis of the evolution equations for the dynamical variables and all the constraints these satisfy in classical General Relativity, that there are no new consistent perfect fluid cosmologies with the kinematic variables and the electric and/or magnetic parts of the Weyl curvature all rotationally symmetric about a common axis in an open neighbourhood Ա of an event. The consistent solutions of this kind are either locally rotationally symmetric, or most generally are subcases of the Szekeres model-an inhomogeneous dust model with no Killing symmetries. This result and its obvious future generalisations provides an input into the equivalence problem in cosmology necessary for a mathematically consistent understanding of probability and a measure set for universes required in quantum cosmology, for instance. We investigate such generalisations and find that similar results hold under some further assumptions dependent on the level of generalisation. In particular, we examine situations where either the electric part or the magnetic part of the free gravitational field are not rotationally symmetric, and also make a brief comment on the most general case where only the shear is rotationally symmetric. We use a tetrad analysis to show that the well-known result that holds for relativistic shear-free dust cosmologies in Einstein's classical theory either the expansion vanishes or the flow is irrotational - has an analogue in the Kaluza-Klein universe model, which has its roots presumably in string theory (or M-theory), recently proposed by Randall and Sundrum. The Big Bang singularity of General Relativity can not be avoided in these so-called brane universes in the situation where we neglect non-local tidal effects on the dynamics by allowing the vorticity to spin up as the singularity is approached in shear-free cases. Moreover, we show that in the general case of a shearing perfect fluid, the singularity at the start of the universe is approached even more strongly than in classical General Relativity in the case of no tidal interaction. Finally, we reconsider the issue of proving large scale spatial homogeneity of the universe in classical General Relativity, given isotropic observations about us and the possibility of source evolution both in numbers and luminosities. We use a spherically symmetric dust universe model (compatible with observations) for our investigation and we solve the field equations on the null cone analytically for the first time. Two theorems make precise the freedom available in constructing cosmological models that will fit the observations. They make quite clear that homogeneity cannot be proven without either a fully determinate theory of source evolution, or availability of distance measures that are independent of source evolution. We contrast this goal with the standard approach that assumes spatial homogeneity a priori, and determines source evolution functions on the basis of this assumption

Large Scale Inhomogeneity Versus Source Evolution -- Can We Distinguish Them Observationally?

We reconsider the issue of proving large scale spatial homogeneity of the universe, given isotropic observations about us and the possibility of source evolution both in numbers and luminosities. Two theorems make precise the freedom available in constructing cosmological models that will fit the observations. They make quite clear that homogeneity cannot be proven without either a fully determinate theory of source evolution, or availability of distance measures that are independent of source evolution. We contrast this goal with the standard approach that assumes spatial homogeneity a priori, and determines source evolution functions on the basis of this assumption.Comment: mn style, mn.sty file included, mn.sty file remove

Partially locally rotationally symmetric perfect fluid cosmologies

We show that there are no new consistent cosmological perfect fluid solutions when in an open neighbourhood ${\cal U}$ of an event the fluid kinematical variables and the electric and magnetic Weyl curvature are all assumed rotationally symmetric about a common spatial axis, specialising the Weyl curvature tensor to algebraic Petrov type D. The consistent solutions of this kind are either locally rotationally symmetric, or are subcases of the Szekeres dust models. Parts of our results require the assumption of a barotropic equation of state. Additionally we demonstrate that local rotational symmetry of perfect fluid cosmologies follows from rotational symmetry of the Riemann curvature tensor and of its covariant derivatives only up to second order, thus strengthening a previous result.Comment: 20 pages, LaTeX2.09 (10pt), no figures; shortened revised version, new references; accepted for publication in Classical and Quantum Gravit

The development and production of GDP flash estimates in a newly industrialised country: the case of South Africa

The experience accumulated from the development and production of a flash estimate of GDP as an official statistic at Statistics South Africa (Stats SA) is presented and discussed. This experience could inform national statistical organisations operating under similar statistical production constraints in other newly industrialised countries or elsewhere. The use of the flash estimate as an early indicator of business cycle slowdowns and upturns is also presented to demonstrate one possible by-product use of the flash estimate

R&D the biggest business casualty of Covid-19?

While the overall economic impact of the Covid-19 pandemic is still unfolding, there are strong indications that it is causing the largest economic downturn since the 2008 financial crisis. In 2020, the South African government implemented lockdown regulations, to safeguard the population, but had adverse effects on businesses and economic activity at large. This brief assesses the effects on firms with research and development (R&D) activity, and appeals for action to protect the national system of innovation

Shrinking II -- The Distortion of the Area Distance-Redshift Relation in Inhomogeneous Isotropic Universes

This paper and the others in the series challenge the standard model of the effects of gravitational lensing on observations at large distances. We show that due to the cumulative effect of lensing, areas corresponding to an observed solid angle can be quite different than would be estimated from the corresponding Friedmann-Lema\^{\i}tre model, even when averaged over large angular scales. This paper concentrates on the specific example of spherically symmetric but spatially inhomogeneous dust universes, the Lema\^{\i}tre-Tolman-Bondi models, and shows that radial lensing significantly distorts the area distance-redshift and density-redshift relations in these exact solutions compared with the standard ones for Friedmann-Lema\^{\i}tre models. Thus inhomogeneity may introduce significant errors into distance estimates based on the standard FL relations, even after all-sky averaging. In addition a useful new gauge choice is presented for these models, solving the problem of locating the past null cone exactly.Comment: Minor technical refinement, 16 pages, RevTex, 8 eps figure

Clumps into Voids

We consider a spherically symmetric distribution of dust and show that it is possible, under general physically reasonable conditions, for an overdensity to evolve to an underdensity (and vice versa). We find the conditions under which this occurs and illustrate it on a class of regular Lemaitre-Tolman-Bondi solutions. The existence of this phenomenon, if verified, would have the result that the topology of density contours, assumed fixed in standard structure formation theories, would have to change and that luminous matter would not trace the dark matter distribution so well.Comment: LaTeX, 17 pages, 4 figures. Submitted to GRG 20/4/200

Multinational corporations as channels for international technology transfer: Evidence from the South African innovation survey

In this article, we investigate the importance of South African subsidiaries of foreign multinationals as channels to introduce foreign innovations in the South African market. We use firm-level data from the 2008 wave of the South African Innovation Survey, which covers the period 2005-07. We find that subsidiaries of foreign multinationals are significantly more likely to introduce product and process innovations, as well as foreign new products and processes than domestic firms. However, we also find that they are not more likely to introduce foreign innovations developed in collaboration with or mostly by another firm outside their own multinational, or innovations that are new to the South African market