Poverty, inequality, child abuse and neglect: changing the conversation across the UK in child protection?

This article explores the evidence on the relationship between poverty, inequality and child abuse and neglect. It argues for the importance of developing further work on the implications of inequality, in particular, as this is a significantly underdeveloped area of study despite compelling evidence of its pertinence to the harms that children and their families experience. Drawing from the findings of a quantitative study that an 'inverse intervention law' seemed to be in operation with systematic unequal implications for children, the conceptual thinking behind a new qualitative study to explore why and how this law operates is explained. The implications for policy and practice are discussed in order to promote further debate about what is often a neglected or invisible aspect of child protection

Uniqueness properties of the Kerr metric

We obtain a geometrical condition on vacuum, stationary, asymptotically flat spacetimes which is necessary and sufficient for the spacetime to be locally isometric to Kerr. Namely, we prove a theorem stating that an asymptotically flat, stationary, vacuum spacetime such that the so-called Killing form is an eigenvector of the self-dual Weyl tensor must be locally isometric to Kerr. Asymptotic flatness is a fundamental hypothesis of the theorem, as we demonstrate by writing down the family of metrics obtained when this requirement is dropped. This result indicates why the Kerr metric plays such an important role in general relativity. It may also be of interest in order to extend the uniqueness theorems of black holes to the non-connected and to the non-analytic case.Comment: 30 pages, LaTeX, submitted to Classical and Quantum Gravit

Uniqueness Theorem for Static Black Hole Solutions of sigma-models in Higher Dimensions

We prove the uniqueness theorem for self-gravitating non-linear sigma-models in higher dimensional spacetime. Applying the positive mass theorem we show that Schwarzschild-Tagherlini spacetime is the only maximally extended, static asymptotically flat solution with non-rotating regular event horizon with a constant mapping.Comment: 5 peges, Revtex, to be published in Class.Quantum Gra

Towards the classification of static vacuum spacetimes with negative cosmological constant

We present a systematic study of static solutions of the vacuum Einstein equations with negative cosmological constant which asymptotically approach the generalized Kottler (``Schwarzschild--anti-de Sitter'') solution, within (mainly) a conformal framework. We show connectedness of conformal infinity for appropriately regular such space-times. We give an explicit expression for the Hamiltonian mass of the (not necessarily static) metrics within the class considered; in the static case we show that they have a finite and well defined Hawking mass. We prove inequalities relating the mass and the horizon area of the (static) metrics considered to those of appropriate reference generalized Kottler metrics. Those inequalities yield an inequality which is opposite to the conjectured generalized Penrose inequality. They can thus be used to prove a uniqueness theorem for the generalized Kottler black holes if the generalized Penrose inequality can be established.Comment: the discussion of our results includes now some solutions of Horowitz and Myers; typos corrected here and there; a shortened version of this version will appear in Journal of Mathematical Physic

Uniqueness and non-uniqueness of static vacuum black holes in higher dimensions

We prove the uniqueness theorem for asymptotically flat static vacuum black hole solutions in higher dimensional space-times. We also construct infinitely many non-asymptotically flat regular static black holes on the same spacetime manifold with the same spherical topology.Comment: to appear in Progress of Theoretical Physics Supplement No. 14

A Mass Bound for Spherically Symmetric Black Hole Spacetimes

Requiring that the matter fields are subject to the dominant energy condition, we establish the lower bound $(4\pi)^{-1} \kappa {\cal A}$ for the total mass $M$ of a static, spherically symmetric black hole spacetime. (${\cal A}$ and $\kappa$ denote the area and the surface gravity of the horizon, respectively.) Together with the fact that the Komar integral provides a simple relation between $M - (4\pi)^{-1} \kappa A$ and the strong energy condition, this enables us to prove that the Schwarzschild metric represents the only static, spherically symmetric black hole solution of a selfgravitating matter model satisfying the dominant, but violating the strong energy condition for the timelike Killing field $K$ at every point, that is, $R(K,K) \leq 0$. Applying this result to scalar fields, we recover the fact that the only black hole configuration of the spherically symmetric Einstein-Higgs model with arbitrary non-negative potential is the Schwarzschild spacetime with constant Higgs field. In the presence of electromagnetic fields, we also derive a stronger bound for the total mass, involving the electromagnetic potentials and charges. Again, this estimate provides a simple tool to prove a ``no-hair'' theorem for matter fields violating the strong energy condition.Comment: 16 pages, LATEX, no figure

FUNGIBLE AND COMPATIBLE BIOFUELS: LITERATURE SEARCH, SUMMARY, AND RECOMMENDATIONS

The purpose of the study described in this report is to summarize the various barriers to more widespread distribution of bio-fuels through our common carrier fuel distribution system, which includes pipelines, barges and rail, fuel tankage, and distribution terminals. Addressing these barriers is necessary to allow the more widespread utilization and distribution of bio-fuels, in support of a renewable fuels standard and possible future low-carbon fuel standards. These barriers can be classified into several categories, including operating practice, regulatory, technical, and acceptability barriers. Possible solutions to these issues are discussed; including compatibility evaluation, changes to bio-fuels, regulatory changes, and changes in the distribution system or distribution practices. No actual experimental research has been conducted in the writing of this report, but results are used to develop recommendations for future research and additional study as appropriate. This project addresses recognized barriers to the wider use of bio-fuels in the areas of development of codes and standards, industrial and consumer awareness, and materials compatibility issues

THE UNIQUENESS THEOREM FOR ROTATING BLACK HOLE SOLUTIONS OF SELF-GRAVITATING HARMONIC MAPPINGS

We consider rotating black hole configurations of self-gravitating maps from spacetime into arbitrary Riemannian manifolds. We first establish the integrability conditions for the Killing fields generating the stationary and the axisymmetric isometry (circularity theorem). Restricting ourselves to mappings with harmonic action, we subsequently prove that the only stationary and axisymmetric, asymptotically flat black hole solution with regular event horizon is the Kerr metric. Together with the uniqueness result for non-rotating configurations and the strong rigidity theorem, this establishes the uniqueness of the Kerr family amongst all stationary black hole solutions of self-gravitating harmonic mappings.Comment: 18 pages, latex, no figure

Untangling child welfare inequalities and the ‘Inverse Intervention Law’ in England

This article addresses some potential limitations of key findings from recent research into inequalities in children’s social services by providing additional evidence from multilevel models that suggest the socioeconomic social gradient and ‘Inverse Intervention Law’ in children’s services interventions are statistically significant after controlling for possible confounding spatial and population effects. Multilevel negative binomial regression models are presented using English child welfare data to predict the following intervention rates at lower super output area-level: Child in Need (n = 2707, middle super output area [MSOA] n = 543, local authority [LA] n = 13); Child Protection Plan (n = 4115, MSOA n = 837, LA n = 18); and Children Looked After (n = 4115, MSOA n = 837, LA n = 18). We find strong evidence supporting the existence of a steep socioeconomic social gradient in child welfare interventions. Furthermore, we find certain local authority contexts exacerbate this social gradient. Contexts of low overall deprivation and high income inequality are associated with greater socioeconomic inequalities in neighbourhood intervention rates. The relationship between neighbourhood deprivation and children looked after rates is almost five times stronger in local authorities with these characteristics than it is in local authorities with high overall deprivation and low income inequality. We argue that social policy responses addressing structural determinants of child welfare inequalities are needed, and that strategies to reduce the numbers of children taken into care must address underlying poverty and income inequality at both a local and national level

Black hole uniqueness theorems and new thermodynamic identities in eleven dimensional supergravity

We consider stationary, non-extremal black holes in 11-dimensional supergravity having isometry group $\mathbb{R} \times U(1)^8$. We prove that such a black hole is uniquely specified by its angular momenta, its electric charges associated with the various 7-cycles in the manifold, together with certain moduli and vector valued winding numbers characterizing the topological nature of the spacetime and group action. We furthermore establish interesting, non-trivial, relations between the thermodynamic quantities associated with the black hole. These relations are shown to be a consequence of the hidden $E_{8(+8)}$ symmetry in this sector of the solution space, and are distinct from the usual "Smarr-type" formulas that can be derived from the first law of black hole mechanics. We also derive the "physical process" version of this first law applicable to a general stationary black hole spacetime without any symmetry assumptions other than stationarity, allowing in particular arbitrary horizon topologies. The work terms in the first law exhibit the topology of the horizon via the intersection numbers between cycles of various dimensions.Comment: 50pp, 3 figures, v2: references added, correction in appendix B, conclusions added, v3: reference section edited, typos removed, minor changes in appendix