Stationary Bianchi type II perfect fluid models

Einstein's field equations for stationary Bianchi type II models with a perfect fluid source are investigated. The field equations are rewritten as a system of autonomous first order differential equations. Dimensionless variables are subsequently introduced for which the reduced phase space is compact. The system is then studied qualitatively using the theory of dynamical systems. It is shown that the locally rotationally symmetric models are not asymptotically self-similar for small values of the independent , tovariable. A new exact solution is also given.Comment: 6 pages, 1 figure LaTeX. To appear in JM

The nature of gravitational singularities

The nature of gravitational singularities, long mysterious, has now become clear through a combination of mathematical and numerical analysis. As the singularity is approached, the time derivative terms in the field equations dominate, and the singularity behaves locally like a homogeneous oscillatory spacetime.Comment: received "honorable mention" in Gravity Research Foundation essay contes

Spherically symmetric relativistic stellar structures

We investigate relativistic spherically symmetric static perfect fluid models in the framework of the theory of dynamical systems. The field equations are recast into a regular dynamical system on a 3-dimensional compact state space, thereby avoiding the non-regularity problems associated with the Tolman-Oppenheimer-Volkoff equation. The global picture of the solution space thus obtained is used to derive qualitative features and to prove theorems about mass-radius properties. The perfect fluids we discuss are described by barotropic equations of state that are asymptotically polytropic at low pressures and, for certain applications, asymptotically linear at high pressures. We employ dimensionless variables that are asymptotically homology invariant in the low pressure regime, and thus we generalize standard work on Newtonian polytropes to a relativistic setting and to a much larger class of equations of state. Our dynamical systems framework is particularly suited for numerical computations, as illustrated by several numerical examples, e.g., the ideal neutron gas and examples that involve phase transitions.Comment: 23 pages, 25 figures (compressed), LaTe

Parental investment in child health in sub-Saharan Africa: a cross-national study of health-seeking behaviour

Parents face trade-offs between investing in child health and other fitness enhancing activities. In humans, parental investment theory has mostly been examined through the analysis of differential child outcomes, with less emphasis on the actions parents take to further a particular offspring's condition. Here, we make use of household data on health-seeking for children in a high mortality context where such behaviours are crucial for offspring survival. Using Demographic and Health Survey (DHS) data from 17 sub-Saharan African countries, we examine whether maternal factors (age, health, marital status) and child factors (birth order, health, sex, age) independently influence parental investment in health-seeking behaviours: two preventative behaviours (malaria net use and immunization) and two curative ones (treating fever and diarrhoea). Results indicate that children with lower birth order, older mothers and mothers with better health status have higher odds of investment. The effects of a child's sex and health status and whether the mother is polygynously married vary depending on the type of health-seeking behaviour (preventative versus curative). We discuss how these results square with predictions from parental investment theory pertaining to the state of mothers and children, and reflect on some potential mechanisms and directions for future research

Effects of local extrinsic mortality rate, crime and sex ratio on preventable death in Northern Ireland

BACKGROUND AND OBJECTIVES: Individual investment in health varies greatly within populations and results in significant differences in the risk of preventable death. Life history theory predicts that individuals should alter their investment in health (somatic maintenance) in response to ecological cues that shift the perceived fitness payoffs to such investments. However, previous research has failed to isolate the effects of different ecological factors on preventable death, and has often relied on macro-level data without individual controls. Here, we test some key predictions concerning the local ecology-that higher extrinsic mortality rate (EMR), crime rate and mate-scarcity (male/female-biased sex ratio) at the ward-level-will be associated with a higher risk of preventable death. METHODOLOGY: We use census-based data from Northern Ireland (n = 927 150) on preventable death during an 8.7-year period from the 2001 Census and run Cox regressions for (i) accident/suicide or alcohol-related death and (ii) deaths from preventable diseases, for men and women separately, controlling for a wide range of individual variables. RESULTS: We find evidence of ward-level EMR and crime rate being positively associated with preventable death among men, particularly men with low socioeconomic position. There was a tentative relationship between male-biased sex ratio and preventable death among women, but not among men. CONCLUSION AND IMPLICATIONS: Both behaviours that might lead to 'risky' death and health neglect might be adaptive responses to local ecologies. Efforts to reduce crime might be as effective as those to reduce extrinsic mortality, and both could have positive effects on various health behaviours

Parental investment in child health in sub-Saharan Africa: a cross-national study of health-seeking behaviour

Parents face trade-offs between investing in child health and other fitness enhancing activities. In humans, parental investment theory has mostly been examined through the analysis of differential child outcomes, with less emphasis on the actions parents take to further a particular offspring's condition. Here, we make use of household data on health-seeking for children in a high mortality context where such behaviours are crucial for offspring survival. Using Demographic and Health Survey (DHS) data from 17 sub-Saharan African countries, we examine whether maternal factors (age, health, marital status) and child factors (birth order, health, sex, age) independently influence parental investment in health-seeking behaviours: two preventative behaviours (malaria net use and immunization) and two curative ones (treating fever and diarrhoea). Results indicate that children with lower birth order, older mothers and mothers with better health status have higher odds of investment. The effects of a child's sex and health status and whether the mother is polygynously married vary depending on the type of health-seeking behaviour (preventative versus curative). We discuss how these results square with predictions from parental investment theory pertaining to the state of mothers and children, and reflect on some potential mechanisms and directions for future research

Perfect fluids and generic spacelike singularities

We present the conformally 1+3 Hubble-normalized field equations together with the general total source equations, and then specialize to a source that consists of perfect fluids with general barotropic equations of state. Motivating, formulating, and assuming certain conjectures, we derive results about how the properties of fluids (equations of state, momenta, angular momenta) and generic spacelike singularities affect each other.Comment: Considerable changes have been made in presentation and arguments, resulting in sharper conclusion

Matter and dynamics in closed cosmologies

To systematically analyze the dynamical implications of the matter content in cosmology, we generalize earlier dynamical systems approaches so that perfect fluids with a general barotropic equation of state can be treated. We focus on locally rotationally symmetric Bianchi type IX and Kantowski-Sachs orthogonal perfect fluid models, since such models exhibit a particularly rich dynamical structure and also illustrate typical features of more general cases. For these models, we recast Einstein's field equations into a regular system on a compact state space, which is the basis for our analysis. We prove that models expand from a singularity and recollapse to a singularity when the perfect fluid satisfies the strong energy condition. When the matter source admits Einstein's static model, we present a comprehensive dynamical description, which includes asymptotic behavior, of models in the neighborhood of the Einstein model; these results make earlier claims about ``homoclinic phenomena and chaos'' highly questionable. We also discuss aspects of the global asymptotic dynamics, in particular, we give criteria for the collapse to a singularity, and we describe when models expand forever to a state of infinite dilution; possible initial and final states are analyzed. Numerical investigations complement the analytical results