Magnification relations for Kerr lensing and testing Cosmic Censorship

A Kerr black hole with mass parameter m and angular momentum parameter a acting as a gravitational lens gives rise to two images in the weak field limit. We study the corresponding magnification relations, namely the signed and absolute magnification sums and the centroid up to post-Newtonian order. We show that there are post-Newtonian corrections to the total absolute magnification and centroid proportional to a/m, which is in contrast to the spherically symmetric case where such corrections vanish. Hence we also propose a new set of lensing observables for the two images involving these corrections, which should allow measuring a/m with gravitational lensing. In fact, the resolution capabilities needed to observe this for the Galactic black hole should in principle be accessible to current and near-future instrumentation. Since a/m >1 indicates a naked singularity, a most interesting application would be a test of the Cosmic Censorship conjecture. The technique used to derive the image properties is based on the degeneracy of the Kerr lens and a suitably displaced Schwarzschild lens at post-Newtonian order. A simple physical explanation for this degeneracy is also given.Comment: 13 pages, version 2: references added, minor changes. To appear in Phys. Rev.

The Geometry of Warped Product Singularities

In this article the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.Comment: 14 page

Band gap control via tuning of inversion degree in CdIn2_2S4_4 spinel

Based on theoretical arguments we propose a possible route for controlling the band-gap in the promising photovoltaic material CdIn$_2$S$_4$. Our \textit{ab initio} calculations show that the experimental degree of inversion in this spinel (fraction of tetrahedral sites occupied by In) corresponds approximately to the equilibrium value given by the minimum of the theoretical inversion free energy at a typical synthesis temperature. Modification of this temperature, or of the cooling rate after synthesis, is then expected to change the inversion degree, which in turn sensitively tunes the electronic band-gap of the solid, as shown here by accurate screened hybrid functional calculations.Comment: In press in Applied Physics Letters (2012); 4 pages, 2 figures, 1 tabl

Causes of Prolonged Waiting Time in Public Health Facilities among Health Care Seekers in Calabar Municipal Council of Cross River State, Nigeria

The purpose of this study was to investigate the causes of prolonged waiting time in public health care facilities among health care seekers in Calabar Municipal Council of Cross River State, Nigeria. To carry out this investigation, two hypotheses were formulated to guide the study. Survey research design was adopted for this study. A sample of one hundred and eighteen (118) respondents was selected. The selection was done through cluster sampling technique. The questionnaire was the main instrument used for data collection. It was constructed by the researchers with assistance of some measurement experts that gave it face and content validity. The Chi-square (X2) inferential statistics set at 0.05 was used to test the hypothesis. The result shows that there is significant contribution of poor record keeping and inadequate health personnel to the prolonged waiting time in public health care facilities among health care seekers. Based on these findings, some recommendations and suggestions for further studies were made. Keywords: Prolong waiting time; Public health facilities, Health care seekers. Poor record keeping; inadequate health personnel

Synchrotron radiation study of the relation between structure and strain in polyurethane elastomers

This paper describes a system for the study of the relation between structure and applied strain in thermoplastic polyurethane elastomers using the Australian National Beamline Facility at the Photon Factory, KEK, Tsukuba, Japan. The system uses the sagittal focusing monochromator at beamline 20B to provide a high-intensity focused beam which then falls on the specimen mounted in a miniature tensometer mounted in the unique vacuum diffractometer (BIGDIFF). Imaging plates were used to record simultaneously SAXS and WAXS patterns from the specimen at a particular strain. The change in SAXS and WAXS patterns with loading and unloading was recorded using a ten-plate imaging-plate changer

Linear Stability of Triangular Equilibrium Points in the Generalized Photogravitational Restricted Three Body Problem with Poynting-Robertson Drag

In this paper we have examined the linear stability of triangular equilibrium points in the generalised photogravitational restricted three body problem with Poynting-Robertson drag. We have found the position of triangular equilibrium points of our problem. The problem is generalised in the sense that smaller primary is supposed to be an oblate spheroid. The bigger primary is considered as radiating. The equations of motion are affected by radiation pressure force, oblateness and P-R drag. All classical results involving photogravitational and oblateness in restricted three body problem may be verified from this result. With the help of characteristic equation, we discussed the stability. Finally we conclude that triangular equilibrium points are unstable.Comment: accepted for publication in Journal of Dynamical Systems & Geometric Theories Vol. 4, Number 1 (2006

Halo properties and secular evolution in barred galaxies

The halo plays a crucial role in the evolution of barred galaxies. Its near-resonant material absorbs angular momentum emitted from some of the disc particles and helps the bar become stronger. As a result, a bar (oval) forms in the inner parts of the halo of strongly barred disc galaxies. It is thinner in the inner parts (but still considerably fatter than the disc bar) and tends to spherical at larger radii. Its length increases with time, while always staying shorter than the disc bar. It is roughly aligned with the disc bar, which it trails only slightly, and it turns with roughly the same pattern speed. The bi-symmetric component of the halo density continues well outside the halo bar, where it clearly trails behind the disc bar. The length and strength of the disc and halo bars correlate; the former being always much stronger than the latter. If the halo is composed of weakly interacting massive particles, then the formation of the halo bar, by redistributing the matter in the halo and changing its shape, could influence the expected annihilation signal. This is indeed found to be the case if the halo has a core, but not if it has a steep cusp. The formation and evolution of the bar strongly affect the halo orbits. A fraction of them becomes near-resonant, similar to the disc near-resonant orbits at the same resonance, while another fraction becomes chaotic. Finally, a massive and responsive halo makes it harder for a central mass concentration to destroy the disc bar.Comment: 6 pages, 3 figures, to appear in "Island Universes - Structure and Evolution of Disk Galaxies" ed. R. S. de Jon

Cryptic Diversity and Conservation of Gopher Frogs across the Southeastern United States

Identifying cryptic biodiversity is fundamental to evolutionary biology and to conservation efforts. This study investigated range-wide genetic diversity of Gopher Frogs, Lithobates capito, across the southeastern United States coastal plain to determine implications for taxonomy and conservation. We collected data for two mtDNA regions in 21 populations to identify genetic structure across the geographic distribution of the species. Based on population genetic, phylogenetic, and genealogical analyses, we recovered three reciprocally monophyletic mtDNA lineages corresponding to mainland coastal plain populations and two lineages within peninsular Florida. Breakpoints for these lineages did not occur in previously identified hotspots of amphibian phylogeographic breaks and did not follow currently recognized subspecies designations. We recommend these lineages be recognized as separate distinct population segments and be considered separately by the U.S. Fish and Wildlife Service for listing under the Endangered Species Act. Additionally, we propose an evolutionary hotspot for amphibians that deserves further attentio