Dynamical extensions for shell-crossing singularities

We derive global weak solutions of Einstein's equations for spherically symmetric dust-filled space-times which admit shell-crossing singularities. In the marginally bound case, the solutions are weak solutions of a conservation law. In the non-marginally bound case, the equations are solved in a generalized sense involving metric functions of bounded variation. The solutions are not unique to the future of the shell-crossing singularity, which is replaced by a shock wave in the present treatment; the metric is bounded but not continuous.Comment: 14 pages, 1 figur

Space-time extensions II

The global extendibility of smooth causal geodesically incomplete spacetimes is investigated. Denote by $\gamma$ one of the incomplete non-extendible causal geodesics of a causal geodesically incomplete spacetime $(M,g_{ab})$. First, it is shown that it is always possible to select a synchronised family of causal geodesics $\Gamma$ and an open neighbourhood $\mathcal{U}$ of a final segment of $\gamma$ in $M$ such that $\mathcal{U}$ is comprised by members of $\Gamma$, and suitable local coordinates can be defined everywhere on $\mathcal{U}$ provided that $\gamma$ does not terminate either on a tidal force tensor singularity or on a topological singularity. It is also shown that if, in addition, the spacetime, $(M,g_{ab})$, is globally hyperbolic, and the components of the curvature tensor, and its covariant derivatives up to order $k-1$ are bounded on $\mathcal{U}$, and also the line integrals of the components of the $k^{th}$-order covariant derivatives are finite along the members of $\Gamma$---where all the components are meant to be registered with respect to a synchronised frame field on $\mathcal{U}$---then there exists a $C^{k-}$ extension $\Phi: (M,g_{ab}) \rightarrow (\widehat{M},\widehat{g}_{ab})$ so that for each $\bar\gamma\in\Gamma$, which is inextendible in $(M,g_{ab})$, the image, $\Phi\circ\bar\gamma$, is extendible in $(\widehat{M},\widehat{g}_{ab})$. Finally, it is also proved that whenever $\gamma$ does terminate on a topological singularity $(M,g_{ab})$ cannot be generic.Comment: 42 pages, no figures, small changes to match the published versio

Remarks on the distributional Schwarzschild geometry

This work is devoted to a mathematical analysis of the distributional Schwarzschild geometry. The Schwarzschild solution is extended to include the singularity; the energy momentum tensor becomes a delta-distribution supported at r=0. Using generalized distributional geometry in the sense of Colombeau's (special) construction the nonlinearities are treated in a mathematically rigorous way. Moreover, generalized function techniques are used as a tool to give a unified discussion of various approaches taken in the literature so far; in particular we comment on geometrical issues

Curvature singularity of the distributional BTZ black hole geometry

For the non-rotating BTZ black hole, the distributional curvature tensor field is found. It is shown to have singular parts proportional to a $\delta$-distribution with support at the origin. This singularity is related, through Einstein field equations, to a point source. Coordinate invariance and independence on the choice of differentiable structure of the results are addressed.Comment: Latex, 7 page

Examining the spatiotemporal disruption to gaze when using a myoelectric prosthetic hand

The aim of this study was to provide a detailed account of the spatial and temporal disruptions to eye-hand coordination when using a prosthetic hand during a sequential fine motor skill. Twenty-one abled-bodied participants performed 15 trials of the ‘picking up coins’ task derived from the Southampton Hand Assessment Procedure (SHAP) with their anatomic hand and with a prosthesis simulator while wearing eye-tracking equipment. Gaze behaviour results revealed that when using the prosthesis, performance detriments were accompanied by significantly greater hand-focused gaze and a significantly longer time to disengage gaze from manipulations to plan upcoming movements. Our findings highlight key metrics that distinguish disruptions to eye-hand coordination that might have implications for the training of prosthesis use

Factors associated with self-care activities among adults in the United Kingdom: a systematic review

Background: The Government has promoted self-care. Our aim was to review evidence about who uses self-tests and other self-care activities (over-the-counter medicine, private sector,complementary and alternative medicine (CAM), home blood pressure monitors). Methods: During April 2007, relevant bibliographic databases (Medline, Embase, Cumulative Index to Nursing and Allied Health Literature, Applied Social Sciences Index and Abstracts, PsycINFO,British Nursing Index, Allied and Complementary Medicine Database, Sociological Abstracts, International Bibliography of the Social Sciences, Arthritis and Complementary Medicine Database, Complementary and Alternative Medicine and Pain Database) were searched, and potentially relevant studies were reviewed against eligibility criteria. Studies were included if they were published during the last 15 years and identified factors, reasons or characteristics associated with a relevant activity among UK adults. Two independent reviewers used proformas to assess the quality of eligible studies. Results: 206 potentially relevant papers were identified, 157 were excluded, and 49 papers related to 46 studies were included: 37 studies were, or used data from questionnaire surveys, 36 had quality scores of five or more out of 10, and 27 were about CAM. Available evidence suggests that users of CAM and over-the-counter medicine are female, middle-aged, affluent and/or educated with some measure of poor health, and that people who use the private sector are affluent and/or educated. Conclusion: People who engage in these activities are likely to be affluent. Targeted promotion may, therefore, be needed to ensure that use is equitable. People who use some activities also appear to have poorer measures of health than non-users or people attending conventional services. It is, therefore, also important to ensure that self-care is not used as a second choice for people who have not had their needs met by conventional service

The Ethnic 'Other' in Ukrainian History Textbooks: The Case of Russia and the Russians

This paper examines portrayals of Russia and the Russians in two generations of Ukrainian history textbooks. It observes that the textbooks are highly condemning of Ukraine's main ethnic other in the guise of foreign ruler: the tsarist authorities and the Soviet regime are always attributed dubious and malicious intentions even if there is appreciation for some of their policies. By contrast, the books, certainly those of the second generation, refrain from presenting highly biased accounts of the ethnic other as a national group (i.e. Russians). Instances where negative judgements do fall onto Russians are counterbalanced by excerpts criticizing ethnic Ukrainians or highlighting conflicting interests within the Ukrainian ethnic group. The negative appraisal of the ethnic other as foreign ruler is clearly instrumental for the nation-building project as it sustains a discourse legitimating the existence of Ukraine as independent state. However, recent trends in history education, the paper concludes, suggest that the importance of nurturing patriotism as a national policy objective is diminishing