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

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

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

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

Fish acquisition and consumption in the African Great Lakes Region through a food environment lens: A scoping review

Effective actions for the fishery and aquaculture sectors to contribute toward improving nutrition rely on an understanding of the factors influencing fish intake, particularly amongst vulnerable populations. This scoping review synthesises evidence from 33 studies in the African Great Lakes Region to examine the influence of food environments on fish acquisition and consumption. We identified only two studies that explicitly applied a food environment framework and none that linked policy conditions with the contribution of fish to diets. Economic access to fish was represented in the largest number of included studies (21 studies), followed by preferences, acceptability and desirability of fish (17 studies) and availability and physical access (14 studies). Positive perceptions of taste and low cost, relative to other animal-source foods, were drivers of fish purchases in many settings; however, limited physical and economic access were frequently identified as preventing optimal intake. In lakeside communities, fish were increasingly directed toward external markets which reduced the availability and affordability of fish for local households. Few studies considered intra-household variations in fish access according to age, gender or physiological status, which represents an important knowledge gap. There is also scope for future research on seasonal influences on fish access and the design and rigorous evaluation of programmes and policies that address one or more constraints of availability, cost, convenience and preferences

The classification of static vacuum space-times containing an asymptotically flat spacelike hypersurface with compact interior

We prove non-existence of static, vacuum, appropriately regular, asymptotically flat black hole space-times with degenerate (not necessarily connected) components of the event horizon. This finishes the classification of static, vacuum, asymptotically flat domains of outer communication in an appropriate class of space-times, showing that the domains of outer communication of the Schwarzschild black holes exhaust the space of appropriately regular black hole exteriors.Comment: This version includes an addendum with a corrected proof of non-existence of zeros of the Killing vector at degenerate horizons. A problem with yet another Lemma is pointed out; this problem does not arise if one assumes analyticity of the metric. An alternative solution, that does not require analyticity, has been given in arXiv:1004.0513 [gr-qc] under appropriate global condition

Pollen productivity estimates of key European plant taxa for quantitative reconstruction of past vegetation: a review

International audienceInformation on the spatial distribution of past vegetation on local, regional and global scales is increasingly used within climate modelling, nature conservancy and archaeology. It is possible to obtain such information from fossil pollen records in lakes and bogs using the landscape reconstruction algorithm (LRA) and its two models, REVEALS and LOVE. These models assume that reliable pollen productivity estimates (PPEs) are available for the plant taxa involved in the quantitative reconstruc -tions of past vegetation, and that PPEs are constant through time. This paper presents and discusses the PPEs for 15 tree and 18 herb taxa obtained in nine study areas of Europe. Observed differences in PPEs between regions may be explained by methodological issues and environmental variables, of which climate and related factors such as reproduction strategies and growth forms appear to be the most important. An evaluation of the PPEs at hand so far suggests that they can be used in modelling applications and quantitative reconstructions of pastvegetation, provided that consideration of past environmental variability within the region is used to inform selection of PPEs, and bearing in mind that PPEs might have changed through time as a response to climate change. Application of a range of possible PPEs will allow a better evaluation of the results

To what extent is behaviour a problem in English schools?:Exploring the scale and prevalence of deficits in classroom climate

The working atmosphere in the classroom is an important variable in the process of education in schools, with several studies suggesting that classroom climate is an important influence on pupil attainment. There are wide differences in the extent to which classroom climate is considered to be a problem in English schools. Some ‘official’ reports suggest that behaviour in schools is ‘satisfactory or better’ in the vast majority of schools; other sources have pointed to behaviour being a serious and widespread problem. The paper details four studies conducted over the past decade which aimed to explore these disparities. The aim of the research was to gain a more accurate insight into the extent to which deficits in classroom climate limit educational attainment and equality of educational opportunity in English schools. The findings question the suggestion that behaviour is satisfactory or better in 99.7% of English schools and the concluding section suggests ways in which deficits in classroom climate might be addressed. Although the study is limited to classrooms in England, OECD studies suggest that deficits in the working atmosphere in classrooms occur in many countries. The study therefore has potential relevance for education systems in other countries

A global biophysical typology of mangroves and its relevance for ecosystem structure and deforestation

Mangrove forests provide many ecosystem services but are among the world's most threatened ecosystems. Mangroves vary substantially according to their geomorphic and sedimentary setting; while several conceptual frameworks describe these settings, their spatial distribution has not been quantified. Here, we present a new global mangrove biophysical typology and show that, based on their 2016 extent, 40.5% (54,972 km2) of mangrove systems were deltaic, 27.5% (37,411 km2) were estuarine and 21.0% (28,493 km2) were open coast, with lagoonal mangroves the least abundant (11.0%, 14,993 km2). Mangroves were also classified based on their sedimentary setting, with carbonate mangroves being less abundant than terrigenous, representing just 9.6% of global coverage. Our typology provides a basis for future research to incorporate geomorphic and sedimentary setting in analyses. We present two examples of such applications. Firstly, based on change in extent between 1996 and 2016, we show while all types exhibited considerable declines in area, losses of lagoonal mangroves (- 6.9%) were nearly twice that of other types. Secondly, we quantify differences in aboveground biomass between mangroves of different types, with it being significantly lower in lagoonal mangroves. Overall, our biophysical typology provides a baseline for assessing restoration potential and for quantifying mangrove ecosystem service provision