Asymptotic silence-breaking singularities

We discuss three complementary aspects of scalar curvature singularities: asymptotic causal properties, asymptotic Ricci and Weyl curvature, and asymptotic spatial properties. We divide scalar curvature singularities into two classes: so-called asymptotically silent singularities and non-generic singularities that break asymptotic silence. The emphasis in this paper is on the latter class which have not been previously discussed. We illustrate the above aspects and concepts by describing the singularities of a number of representative explicit perfect fluid solutions.Comment: 25 pages, 6 figure

Gravitational Entropy and Quantum Cosmology

We investigate the evolution of different measures of ``Gravitational Entropy'' in Bianchi type I and Lema\^itre-Tolman universe models. A new quantity behaving in accordance with the second law of thermodynamics is introduced. We then go on and investigate whether a quantum calculation of initial conditions for the universe based upon the Wheeler-DeWitt equation supports Penrose's Weyl Curvature Conjecture, according to which the Ricci part of the curvature dominates over the Weyl part at the initial singularity of the universe. The theory is applied to the Bianchi type I universe models with dust and a cosmological constant and to the Lema\^itre-Tolman universe models. We investigate two different versions of the conjecture. First we investigate a local version which fails to support the conjecture. Thereafter we construct a non-local entity which shows more promising behaviour concerning the conjecture.Comment: 20 pages, 7 ps figure

Intranet Adoption In A Construction SME: So What Actually Happened?

Over 90% of the firms within the UK Construction Industry are small and medium-sized enterprises (SMEs). Whilst larger organisations have recognised the benefits and competitive advantages of information and communications technology, yet struggle to come to terms with adoption barriers, the situation for SMEs appears even more daunting. However, this does not prevent some of the more innovative construction SMEs from trying. The paper reports an action research study conducted over a period of 2 years with such an organisation. The firm had decided to go beyond its former, limited use of ICT (i.e. basic email, accounting, planning software) towards adopting an intranet for the communication of all its management information. Empirical data have been derived from observation, documentary evidence (including the rigorous recording of events in the project’s progress) and recorded conversations. Access was enhanced as the researcher occupied a key role in the project’s implementation. Data will be analysed and interpreted using a SCOT (Social Construction of Technology) theoretical framework, and this work is currently in progress. The conclusions presented here are, therefore, tentative, but suggest that IT adoption success is very dependent on understanding complex cultural issues associated with SME owner management, the lack of ICT management knowledge and the ad-hoc and inconsistent nature of ICT vendor support

Asymptotic self-similarity breaking at late times in cosmology

We study the late time evolution of a class of exact anisotropic cosmological solutions of Einstein's equations, namely spatially homogeneous cosmologies of Bianchi type VII$_0$ with a perfect fluid source. We show that, in contrast to models of Bianchi type VII$_h$ which are asymptotically self-similar at late times, Bianchi VII$_0$ models undergo a complicated type of self-similarity breaking. This symmetry breaking affects the late time isotropization that occurs in these models in a significant way: if the equation of state parameter $\gamma$ satisfies $\gamma \leq 4/3$ the models isotropize as regards the shear but not as regards the Weyl curvature. Indeed these models exhibit a new dynamical feature that we refer to as Weyl curvature dominance: the Weyl curvature dominates the dynamics at late times. By viewing the evolution from a dynamical systems perspective we show that, despite the special nature of the class of models under consideration, this behaviour has implications for more general models.Comment: 29 page

Conformal regularization of Einstein's field equations

To study asymptotic structures, we regularize Einstein's field equations by means of conformal transformations. The conformal factor is chosen so that it carries a dimensional scale that captures crucial asymptotic features. By choosing a conformal orthonormal frame we obtain a coupled system of differential equations for a set of dimensionless variables, associated with the conformal dimensionless metric, where the variables describe ratios with respect to the chosen asymptotic scale structure. As examples, we describe some explicit choices of conformal factors and coordinates appropriate for the situation of a timelike congruence approaching a singularity. One choice is shown to just slightly modify the so-called Hubble-normalized approach, and one leads to dimensionless first order symmetric hyperbolic equations. We also discuss differences and similarities with other conformal approaches in the literature, as regards, e.g., isotropic singularities.Comment: New title plus corrections and text added. To appear in CQ

Self-similar Bianchi models: I. Class A models

We present a study of Bianchi class A tilted cosmological models admitting a proper homothetic vector field together with the restrictions, both at the geometrical and dynamical level, imposed by the existence of the simply transitive similarity group. The general solution of the symmetry equations and the form of the homothetic vector field are given in terms of a set of arbitrary integration constants. We apply the geometrical results for tilted perfect fluids sources and give the general Bianchi II self-similar solution and the form of the similarity vector field. In addition we show that self-similar perfect fluid Bianchi VII$_0$ models and irrotational Bianchi VI$_0$ models do not exist.Comment: 14 pages, Latex; to appear in Classical and Quantum Gravit

Matter and dynamics in closed cosmologies

To systematically analyze the dynamical implications of the matter content in cosmology, we generalize earlier dynamical systems approaches so that perfect fluids with a general barotropic equation of state can be treated. We focus on locally rotationally symmetric Bianchi type IX and Kantowski-Sachs orthogonal perfect fluid models, since such models exhibit a particularly rich dynamical structure and also illustrate typical features of more general cases. For these models, we recast Einstein's field equations into a regular system on a compact state space, which is the basis for our analysis. We prove that models expand from a singularity and recollapse to a singularity when the perfect fluid satisfies the strong energy condition. When the matter source admits Einstein's static model, we present a comprehensive dynamical description, which includes asymptotic behavior, of models in the neighborhood of the Einstein model; these results make earlier claims about ``homoclinic phenomena and chaos'' highly questionable. We also discuss aspects of the global asymptotic dynamics, in particular, we give criteria for the collapse to a singularity, and we describe when models expand forever to a state of infinite dilution; possible initial and final states are analyzed. Numerical investigations complement the analytical results.Comment: 23 pages, 24 figures (compressed), LaTe

Cylindrically symmetric dust spacetime

We present an explicit exact solution of Einstein's equations for an inhomogeneous dust universe with cylindrical symmetry. The spacetime is extremely simple but nonetheless it has new surprising features. The universe is ``closed'' in the sense that the dust expands from a big-bang singularity but recollapses to a big-crunch singularity. In fact, both singularities are connected so that the whole spacetime is ``enclosed'' within a single singularity of general character. The big-bang is not simultaneous for the dust, and in fact the age of the universe as measured by the dust particles depends on the spatial position, an effect due to the inhomogeneity, and their total lifetime has no non-zero lower limit. Part of the big-crunch singularity is naked. The metric depends on a parameter and contains flat spacetime as a non-singular particular case. For appropriate values of the parameter the spacetime is a small perturbation of Minkowski spacetime. This seems to indicate that flat spacetime may be unstable against some global {\it non-vacuum} perturbations.Comment: LaTeX, 6 pages, 1 figure. Uses epsfig package. Submitted to Classical and Quantum Gravit

Spherically symmetric relativistic stellar structures

We investigate relativistic spherically symmetric static perfect fluid models in the framework of the theory of dynamical systems. The field equations are recast into a regular dynamical system on a 3-dimensional compact state space, thereby avoiding the non-regularity problems associated with the Tolman-Oppenheimer-Volkoff equation. The global picture of the solution space thus obtained is used to derive qualitative features and to prove theorems about mass-radius properties. The perfect fluids we discuss are described by barotropic equations of state that are asymptotically polytropic at low pressures and, for certain applications, asymptotically linear at high pressures. We employ dimensionless variables that are asymptotically homology invariant in the low pressure regime, and thus we generalize standard work on Newtonian polytropes to a relativistic setting and to a much larger class of equations of state. Our dynamical systems framework is particularly suited for numerical computations, as illustrated by several numerical examples, e.g., the ideal neutron gas and examples that involve phase transitions.Comment: 23 pages, 25 figures (compressed), LaTe