Dimension-Dependence of the Critical Exponent in Spherically Symmetric Gravitational Collapse

We study the critical behaviour of spherically symmetric scalar field collapse to black holes in spacetime dimensions other than four. We obtain reliable values for the scaling exponent in the supercritical region for dimensions in the range $3.5\leq D\leq 14$. The critical exponent increases monotonically to an asymptotic value at large $D$ of $\gamma\sim0.466$. The data is well fit by a simple exponential of the form: $\gamma \sim 0.466(1-e^{-0.408 D})$.Comment: 5 pages, including 7 figures New version contains more data points, one extra graph and more accurate error bars. No changes to result

Quantum Structure of Space Near a Black Hole Horizon

We describe a midi-superspace quantization scheme for generic single horizon black holes in which only the spatial diffeomorphisms are fixed. The remaining Hamiltonian constraint yields an infinite set of decoupled eigenvalue equations: one at each spatial point. The corresponding operator at each point is the product of the outgoing and ingoing null convergences, and describes the scale invariant quantum mechanics of a particle moving in an attractive $1/X^2$ potential. The variable $X$ that is analoguous to particle position is the square root of the conformal mode of the metric. We quantize the theory via Bohr quantization, which by construction turns the Hamiltonian constraint eigenvalue equation into a finite difference equation. The resulting spectrum gives rise to a discrete spatial topology exterior to the horizon. The spectrum approaches the continuum in the asymptotic region.Comment: References added and typos corrected. 21 pages, 1 figur

Anti-deSitter gravitational collapse

We describe a formalism for studying spherically symmetric collapse of the massless scalar field in any spacetime dimension, and for any value of the cosmological constant $\Lambda$. The formalism is used for numerical simulations of gravitational collapse in four spacetime dimensions with negative $\Lambda$. We observe critical behaviour at the onset of black hole formation, and find that the critical exponent is independent of $\Lambda$.Comment: 4 pages, 2 figures, revtex4, version to appear in CQ

Spherically symmetric scalar field collapse in any dimension

We describe a formalism and numerical approach for studying spherically symmetric scalar field collapse for arbitrary spacetime dimension d and cosmological constant Lambda. The presciption uses a double null formalism, and is based on field redefinitions first used to simplify the field equations in generic two-dimensional dilaton gravity. The formalism is used to construct code in which d and Lambda are input parameters. The code reproduces known results in d = 4 and d = 6 with Lambda = 0. We present new results for d = 5 with zero and negative Lambda.Comment: 16 pages, 6 figures, typos corrected, presentational changes, PRD in pres

Quantum Hamiltonian for gravitational collapse

Using a Hamiltonian formulation of the spherically symmetric gravity-scalar field theory adapted to flat spatial slicing, we give a construction of the reduced Hamiltonian operator. This Hamiltonian, together with the null expansion operators presented in an earlier work, form a framework for studying gravitational collapse in quantum gravity. We describe a setting for its numerical implementation, and discuss some conceptual issues associated with quantum dynamics in a partial gauge fixing.Comment: 17 pages, published version (minor changes

Health and cancer prevention: knowledge and beliefs of children and young people

Objective: To collect information from children and young people about their knowledge of and attitudes towards cancer and their understanding of health and health related behaviours to inform future health promotion work. Design: Questionnaire survey of 15-16 year olds, and interviews with play materials with 9-10 year old children. Setting: Six inner city, suburban, and rural schools. Subjects: 226 children aged 15-16 years and 100 aged 9-10 years. Main outcome measures: Knowledge about different types of cancer; beliefs about health; sources of information; quality of research data obtainable from young children about cancer and health. Results: Both samples knew most about lung cancer, but there was also some knowledge of breast and skin cancer and leukaemia. Smoking, together with pollution and other environmental factors, were seen as the dominant causes of cancer. Environmental factors were mentioned more often by the inner city samples. Television and the media were the most important sources of information. Young people were more worried about unemployment than about ill health. More than half the young people did not describe their health as good, and most said they did not have a healthy lifestyle. Children were able to provide detailed information about their knowledge and understanding by using drawings as well as interviews. Conclusions: Children and young people possess considerable knowledge about cancer, especially about lung cancer and smoking, and show considerable awareness of predominant health education messages. Despite this knowledge, many lead less than healthy lifestyles. Health is not seen as the most important goal in life by many young people; the circumstances in which many children and young people live are not experienced as health promoting

Two dimensional general covariance from three dimensions

A 3d generally covariant field theory having some unusual properties is described. The theory has a degenerate 3-metric which effectively makes it a 2d field theory in disguise. For 2-manifolds without boundary, it has an infinite number of conserved charges that are associated with graphs in two dimensions and the Poisson algebra of the charges is closed. For 2-manifolds with boundary there are additional observables that have a Kac-Moody Poisson algebra. It is further shown that the theory is classically integrable and the general solution of the equations of motion is given. The quantum theory is described using Dirac quantization, and it is shown that there are quantum states associated with graphs in two dimensions.Comment: 10 pages (Latex), Alberta-Thy-19-9

General covariance, and supersymmetry without supersymmetry

An unusual four-dimensional generally covariant and supersymmetric SU(2) gauge theory is described. The theory has propagating degrees of freedom, and is invariant under a local (left-handed) chiral supersymmetry, which is half the supersymmetry of supergravity. The Hamiltonian 3+1 decomposition of the theory reveals the remarkable feature that the local supersymmetry is a consequence of Yang-Mills symmetry, in a manner reminiscent of how general coordinate invariance in Chern-Simons theory is a consequence of Yang-Mills symmetry. It is possible to write down an infinite number of conserved currents, which strongly suggests that the theory is classically integrable. A possible scheme for non-perturbative quantization is outlined. This utilizes ideas that have been developed and applied recently to the problem of quantizing gravity.Comment: 17 pages, RevTeX, two minor errors correcte