The Nature of Generic Cosmological Singularities

The existence of a singularity by definition implies a preferred scale--the affine parameter distance from/to the singularity of a causal geodesic that is used to define it. However, this variable scale is also captured by the expansion along the geodesic, and this can be used to obtain a regularized state space picture by means of a conformal transformation that factors out the expansion. This leads to the conformal `Hubble-normalized' orthonormal frame approach which allows one to translate methods and results concerning spatially homogeneous models into the generic inhomogeneous context, which in turn enables one to derive the dynamical nature of generic cosmological singularities. Here we describe this approach and outline the derivation of the `cosmological billiard attractor,' which describes the generic dynamical asymptotic behavior towards a generic spacelike singularity. We also compare the `dynamical systems picture' resulting from this approach with other work on generic spacelike singularities: the metric approach of Belinskii, Lifschitz, and Khalatnikov, and the recent Iwasawa based Hamiltonian method used by Damour, Henneaux, and Nicolai; in particular we show that the cosmological billiards obtained by the latter and the cosmological billiard attractor form complementary `dual' descriptions of the generic asymptotic dynamics of generic spacelike singularities.Comment: 14 pages, six figures; invited talk at the 11th Marcel Grossmann Meeting on Recent Developments in General Relativity, Berlin, Germany, 23-29 July 200

RISK, UNCERTAINTY, AND SPATIAL DISTINCTION: A STUDY OF URBAN PLANNING IN STOCKHOLM

This paper examines urban planning in Stockholm, focusing on the proposal for a new comprehensive plan. It explores the problems urban planning has set out to solve and whether – and if so, how – the concepts of risk and uncertainty form part of the planning discourse. A departure point is that both urban planning ideals and the problems these ideals claim to address are constructed. Explicitly or implicitly, planning creates demarcations that make places and activities appear safe or risky, attractive or problematic, etc. Analysis of the proposal for a new comprehensive plan for Stockholm identifies at least three such boundaries or spatial distinctions: between centre and periphery, green areas and other parts of the city, and risky or unsafe areas and other areas. Likewise, the analysis finds evidence of a tension between rational planning and normative ideas of the “good city” in urban planning.risk; uncertainty; urban planning.

Stationary Bianchi type II perfect fluid models

Einstein's field equations for stationary Bianchi type II models with a perfect fluid source are investigated. The field equations are rewritten as a system of autonomous first order differential equations. Dimensionless variables are subsequently introduced for which the reduced phase space is compact. The system is then studied qualitatively using the theory of dynamical systems. It is shown that the locally rotationally symmetric models are not asymptotically self-similar for small values of the independent , tovariable. A new exact solution is also given.Comment: 6 pages, 1 figure LaTeX. To appear in JM