Cosmic Strings and Chronology Protection

A space consisting of two rapidly moving cosmic strings has recently been constructed by Gott that contains closed timelike curves. The global structure of this space is analysed and is found that, away from the strings, the space is identical to a generalised Misner space. The vacuum expectation value of the energy momentum tensor for a conformally coupled scalar field is calculated on this generalised Misner space. It is found to diverge very weakly on the Chronology horizon, but more strongly on the polarised hypersurfaces. The divergence on the polarised hypersurfaces is strong enough that when the proper geodesic interval around any polarised hypersurface is of order the Planck length squared, the perturbation to the metric caused by the backreaction will be of order one. Thus we expect the structure of the space will be radically altered by the backreaction before quantum gravitational effects become important. This suggests that Hawking's `Chronology Protection Conjecture' holds for spaces with non-compactly generated Chronology horizon.Comment: 15 pages, plain TeX, 2 figures (not included), DAMTP-R92/3

A Spinorial Hamiltonian Approach to Gravity

We give a spinorial set of Hamiltonian variables for General Relativity in any dimension greater than 2. This approach involves a study of the algebraic properties of spinors in higher dimension, and of the elimination of second-class constraints from the Hamiltonian theory. In four dimensions, when restricted to the positive spin-bundle, these variables reduce to the standard Ashtekar variables. In higher dimensions, the theory can either be reduced to a spinorial version of the ADM formalism, or can be left in a more general form which seems useful for the investigation of some spinorial problems such as Riemannian manifolds with reduced holonomy group. In dimensions $0 \pmod 4$, the theory may be recast solely in terms of structures on the positive spin-bundle $\mathbb{V}^+$, but such a reduction does not seem possible in dimensions $2 \pmod 4$, due to algebraic properties of spinors in these dimensions.Comment: 20 pages, Latex 2e. Published versio

Lsdiff M and the Einstein Equations

We give a formulation of the vacuum Einstein equations in terms of a set of volume-preserving vector fields on a four-manifold ${\cal M}$. These vectors satisfy a set of equations which are a generalisation of the Yang-Mills equations for a constant connection on flat spacetime.Comment: 5 pages, no figures, Latex, uses amsfonts, amssym.def and amssym.tex. Note added on more direct connection with Yang-Mills equation

The ADHM construction and non-local symmetries of the self-dual Yang-Mills equations

We consider the action on instanton moduli spaces of the non-local symmetries of the self-dual Yang-Mills equations on $\mathbb{R}^4$ discovered by Chau and coauthors. Beginning with the ADHM construction, we show that a sub-algebra of the symmetry algebra generates the tangent space to the instanton moduli space at each point. We explicitly find the subgroup of the symmetry group that preserves the one-instanton moduli space. This action simply corresponds to a scaling of the moduli space.Comment: AMSLatex, 19 pages, no figures. Some discussions clarified, and citations made more accurate. I am grateful to the referee for detailed comments. Version to appear in Communications in Mathematical Physic

The emergence of magnetic flux through a partially ionised solar atmosphere

We present results from 2.5D numerical simulations of the emergence of magnetic flux from the upper convection zone through the photosphere and chromosphere into the corona. Certain regions of the solar atmosphere are at sufficiently low temperatures to be only partially ionised, in particular the lower chromosphere. This leads to Cowling resistivities orders of magnitude larger than the Coulomb values, and thus to anisotropic dissipation in Ohm’s law. This also leads to localised low magnetic Reynolds numbers (R m < 1). We find that the rates of emergence of magnetic field are greatly increased by the partially ionised regions of the model atmosphere, and the resultant magnetic field is more diffuse. More importantly, the only currents associated with the magnetic field to emerge into the corona are aligned with the field, and thus the newly formed coronal field is force-free

Web Single Sign-On Authentication using SAML

Companies have increasingly turned to application service providers (ASPs) or Software as a Service (SaaS) vendors to offer specialized web-based services that will cut costs and provide specific and focused applications to users. The complexity of designing, installing, configuring, deploying, and supporting the system with internal resources can be eliminated with this type of methodology, providing great benefit to organizations. However, these models can present an authentication problem for corporations with a large number of external service providers. This paper describes the implementation of Security Assertion Markup Language (SAML) and its capabilities to provide secure single sign-on (SSO) solutions for externally hosted applications

Key pedagogic thinkers: Jean Baudrillard

Jean Baudrillard was born in Reims, France, in 1929, and completed his undergraduate work at the Sorbonne, taking a degree in German. Upon graduation, he taught high school. In the early 1960s, he began graduate studies at the University of Paris, Nanterre, earning his doctorate in sociology in 1966. Baudrillard published 30 books in which he examined various facets of modern society: gender, race, consumerism, politics, the media, and so forth. His focus was semiological—how objects and signs reflect the current human condition. Although Baudrillard did not write about education, his work is nevertheless relevant if we recognize that our educational system is a reflection of society. A Baudrillardian perspective raises the following question: What effect has consumerism had on education? To address this question, we offer some background information related to Baudrillard’s philosophical inquiries. This is followed by our brief analysis of how Baudrillard’s work may provide some potential answers to the above question and of how it can help us interpret the changes that have occurred in education during the modern period. We give special emphasis to The Consumer Society and Simulacra and Simulation

A positive mass theorem for low-regularity Riemannian metrics

We show that the positive mass theorem holds for continuous Riemannian metrics that lie in the Sobolev space $W^{2, n/2}_{loc}$ for manifolds of dimension less than or equal to $7$ or spin-manifolds of any dimension. More generally, we give a (negative) lower bound on the ADM mass of metrics for which the scalar curvature fails to be non-negative, where the negative part has compact support and sufficiently small $L^{n/2}$ norm. We show that a Riemannian metric in $W^{2, p}_{loc}$ for some $p > \frac{n}{2}$ with non-negative scalar curvature in the distributional sense can be approximated locally uniformly by smooth metrics with non-negative scalar curvature. For continuous metrics in $W^{2, n/2}_{loc}$, there exist smooth approximating metrics with non-negative scalar curvature that converge in $L^p_{loc}$ for all $p < \infty$.Comment: 21 pages. The results on the positive mass theorem were announced in arxiv:1205.1302, with a sketch of the proo