Ricci identities in higher dimensions

We explore connections between geometrical properties of null congruences and the algebraic structure of the Weyl tensor in n>4 spacetime dimensions. First, we present the full set of Ricci identities on a suitable "null" frame, thus completing the extension of the Newman-Penrose formalism to higher dimensions. Then we specialize to geodetic null congruences and study specific consequences of the Sachs equations. These imply, for example, that Kundt spacetimes are of type II or more special (like for n=4) and that for odd n a twisting geodetic WAND must also be shearing (in contrast to the case n=4).Comment: 8 pages. v2: typo corrected between Propositions 2 and 3. v3: typo in the last term in the first line of (11f) corrected, missing term on the r.h.s. of (11p) added, first sentence between Propositions 2 and 3 slightly change

A rocket ozonesonde for geophysical research and satellite intercomparison

The in-situ rocketsonde for ozone profile measurements developed and flown for geophysical research and satellite comparison is reviewed. The measurement principle involves the chemiluminescence caused by ambient ozone striking a detector and passive pumping as a means of sampling the atmosphere as the sonde descends through the atmosphere on a parachute. The sonde is flown on a meteorological sounding rocket, and flight data are telemetered via the standard meteorological GMD ground receiving system. The payload operation, sensor performance, and calibration procedures simulating flight conditions are described. An error analysis indicated an absolute accuracy of about 12 percent and a precision of about 8 percent. These are combined to give a measurement error of 14 percent

Race, Age, and Neighborhood Socioeconomic Status in Low Birth Weight Disparities Among Adolescent Mothers: An Intersectional Inquiry

Introduction: Few studies examined socioeconomic contributors to racial disparities in low birth weight outcomes between African-American and Caucasian adolescent mothers. This cross-sectional study examined the intersections of maternal racial status, age, and neighborhood socioeconomic status in explaining these disparities in low birth weight outcomes across a statewide sample of adolescent mothers. Methods: Using data from the North Carolina State Center of Health Statistics for 2010-2011, birth cases for 16,472 adolescents were geocoded by street address and linked to census-tract information from the 2010 United States Census. Multilevel models with interaction terms were used to identify significant associations between maternal racial status, age, and neighborhood socioeconomic status (as defined by census-tract median household income) and low birth weight outcomes across census tracts. Results: Significant racial differences were identified in which African-American adolescents had greater odds of low birth weight outcomes than Caucasian adolescents (OR=1.88, 95% CI 1.64, 2.15). Although racial disparities in low birth weight outcomes remained significant in context of maternal age and neighborhood socioeconomic status, the greatest disparities were found between African-American and Caucasian adolescents that lived in areas of higher socioeconomic status (p Conclusion: These findings indicate that racial disparities in low birth weight outcomes among adolescent mothers can vary by neighborhood socioeconomic status. Further investigations using intersectional frameworks are needed for examining the relationships between neighborhood socioeconomic status and birth outcome disparities among infants born to adolescent mothers

Self-similar Bianchi type VIII and IX models

It is shown that in transitively self-similar spatially homogeneous tilted perfect fluid models the symmetry vector is not normal to the surfaces of spatial homogeneity. A direct consequence of this result is that there are no self-similar Bianchi VIII and IX tilted perfect fluid models. Furthermore the most general Bianchi VIII and IX spacetime which admit a four dimensional group of homotheties is given.Comment: 5 pages, Latex; One reference and minor clarifications added. To appear in General Relativity and Gravitatio

Shear-free, Irrotational, Geodesic, Anisotropic Fluid Cosmologies

General relativistic anisotropic fluid models whose fluid flow lines form a shear-free, irrotational, geodesic timelike congruence are examined. These models are of Petrov type D, and are assumed to have zero heat flux and an anisotropic stress tensor that possesses two distinct non-zero eigenvalues. Some general results concerning the form of the metric and the stress-tensor for these models are established. Furthermore, if the energy density and the isotropic pressure, as measured by a comoving observer, satisfy an equation of state of the form $p = p(\mu)$, with $\frac{dp}{d\mu} \neq -\frac{1}{3}$, then these spacetimes admit a foliation by spacelike hypersurfaces of constant Ricci scalar. In addition, models for which both the energy density and the anisotropic pressures only depend on time are investigated; both spatially homogeneous and spatially inhomogeneous models are found. A classification of these models is undertaken. Also, a particular class of anisotropic fluid models which are simple generalizations of the homogeneous isotropic cosmological models is studied.Comment: 13 pages LaTe

Qualitative Analysis of Viscous Fluid Cosmological Models satisfying the Israel-Stewart theory of Irreversible Thermodynamics

Isotropic and spatially homogeneous viscous fluid cosmological models are investigated using the truncated Israel-Stewart theory of irreversible thermodynamics to model the bulk viscous pressure. The governing system of differential equations is written in terms of dimensionless variables and a set of dimensionless equations of state is then utilized to complete the system. The resulting dynamical system is analyzed using geometric techniques from dynamical systems theory to find the qualitative behaviour of the Friedmann-Robertson-Walker models with bulk viscosity. In these models there exists a free parameter such that the qualitative behaviour of the models can be quite different (for certain ranges of values of this parameter) from that found in models satisfying the Eckart theory studied previously. In addition, the conditions under which the models inflate are investigated.Comment: 29 pages, 8 Encapsulated PostScript Figures, uses the IOP style file

Kinematic Self-Similarity

Self-similarity in general relativity is briefly reviewed and the differences between self-similarity of the first kind and generalized self-similarity are discussed. The covariant notion of a kinematic self-similarity in the context of relativistic fluid mechanics is defined. Various mathematical and physical properties of spacetimes admitting a kinematic self-similarity are discussed. The governing equations for perfect fluid cosmological models are introduced and a set of integrability conditions for the existence of a proper kinematic self-similarity in these models is derived. Exact solutions of the irrotational perfect fluid Einstein field equations admitting a kinematic self-similarity are then sought in a number of special cases, and it is found that; (1) in the geodesic case the 3-spaces orthogonal to the fluid velocity vector are necessarily Ricci-flat and (ii) in the further specialisation to dust the differential equation governing the expansion can be completely integrated and the asymptotic properties of these solutions can be determined, (iii) the solutions in the case of zero-expansion consist of a class of shear-free and static models and a class of stiff perfect fluid (and non-static) models, and (iv) solutions in which the kinematic self-similar vector is parallel to the fluid velocity vector are necessarily Friedmann-Robertson-Walker (FRW) models.Comment: 29 pages, AmsTe

Viscous Bianchi type I universes in brane cosmology

We consider the dynamics of a viscous cosmological fluid in the generalized Randall-Sundrum model for an anisotropic, Bianchi type I brane. To describe the dissipative effects we use the Israel-Hiscock-Stewart full causal thermodynamic theory. By assuming that the matter on the brane obeys a linear barotropic equation of state, and the bulk viscous pressure has a power law dependence on the energy density, the general solution of the field equations can be obtained in an exact parametric form. The obtained solutions describe generally a non-inflationary brane world. In the large time limit the brane Universe isotropizes, ending in an isotropic and homogeneous state. The evolution of the temperature and of the comoving entropy of the Universe is also considered, and it is shown that due to the viscous dissipative processes a large amount of entropy is created in the early stages of evolution of the brane world.Comment: 13 pages, 5 figures, to appear in Class. Quantum Gra