Photon redshift and the appearance of a naked singularity

In this paper we analyze the redshift as observed by an external observer receiving photons which terminate in the past at the naked singularity formed in a Tolman-Bondi dust collapse. Within the context of models considered here it is shown that photons emitted from a weak curvature naked singularity are always finitely redshifted to an external observer. Certain cases of strong curvature naked singularities, including the self-similar one, where the photons are infinitely redshifted are also pointed out.Comment: Latex file, 14 pages, no figures, one change in the reference. Accepted for publication in Phys. Rev.

Examining the socio-economic determinants of adoption of the 'Government Gateway' initiative in the UK

This paper empirically examines the impact of socio-economic determinants upon the adoption of a recent UK e-government initiative, the 'Government Gateway'. The data on five socio-economic characteristics was collected employing a postal survey. The findings of this research suggest that the three variables of age, gender and occupation significantly differentiated the adopters from the non-adopters of the Government Gateway, whilst education and income were found to be non-significant. The implications of the findings are discussed in the context of promoting the adoption of emerging Information and Communication Technologies (ICT) and reducing the digital divide against less privileged parts of the population

Impact of Chemical Fertilizer and Organic Manure on the Germination and Growth of Soybean (Glycine max L.)

After green revolution chemical fertilizers has been used at a great extent in all the crops which decrease the fertility and profile of the soil. Due to various side effects of chemical fertilizers, use of organic fertilizers is an alternative method for the improvement of crop production and maintenance of soil fertility. The aim of the present study was to determine the effects of chemical fertilizer and organic manure on the growth of soybean crop. A total of ten different treatments of both organic manure and chemical fertilizer were used. The various parameters - seed germination, seedling survival, root length and shoot length and seedling height was measured in the present investigation. The results revealed that germination percentage showed increment in nearly all the treatments as compared to the control sets except at highest dose of NPK fertilizer which showed little decrease in germination percentage and was found maximum (97.33%) at optimum dose of vermicompost. The results also showed that survival rate was higher in all treatments than control except at the highest dose of NPK fertilizer in which the survival rate was found minimum (74.38%).Also the root length and seedling height was maximum at the optimum dose of Vermicompost (20%) treated plants and was found minimum in the highest dose (300gm) of NPK fertilizer. The results revealed that the chemical fertilizers at higher doses have deleterious effects on plant growth and development. Organic manures at very high doses checks plant growth but vermicompost had no side effects even at higher doses. Keywords: Vermicompost, NPK, FYM, Soybean, Germinatio

Null Geodesic Expansion in Spherical Gravitational Collapse

We derive an expression for the expansion of outgoing null geodesics in spherical dust collapse and compute the limiting value of the expansion in the approach to singularity formation. An analogous expression is derived for the spherical collapse of a general form of matter. We argue on the basis of these results that the covered as well as the naked singularity solutions arising in spherical dust collapse are stable under small changes in the equation of state.Comment: 10 pages, Latex File, No figure

The final fate of spherical inhomogeneous dust collapse II: Initial data and causal structure of singularity

Further to results in [9], pointing out the role of initial density and velocity distributions towards determining the final outcome of spherical dust collapse, the causal structure of singularity is examined here in terms of evolution of the apparent horizon. We also bring out several related features which throw some useful light towards understanding the nature of this singularity, including the behaviour of geodesic families coming out and some aspects related to the stability of singularity.Comment: Latex file, uses epsf.sty, 15 pages and 3 eps figures. Paragraph on role of smooth functions rewritten. Four references added. To appear in Classical & Quantum Gravit

The Final Fate of Spherical Inhomogeneous Dust Collapse

We examine the role of the initial density and velocity distribution in the gravitational collapse of a spherical inhomogeneous dust cloud. Such a collapse is described by the Tolman-Bondi metric which has two free functions: the `mass-function' and the `energy function', which are determined by the initial density and velocity profile of the cloud. The collapse can end in a black-hole or a naked singularity, depending on the initial parameters characterizing these profiles. In the marginally bound case, we find that the collapse ends in a naked singularity if the leading non-vanishing derivative of the density at the center is either the first one or the second one. If the first two derivatives are zero, and the third derivative non-zero, the singularity could either be naked or covered, depending on a quantity determined by the third derivative and the central density. If the first three derivatives are zero, the collapse ends in a black hole. In particular, the classic result of Oppenheimer and Snyder, that homogeneous dust collapse leads to a black hole, is recovered as a special case. Analogous results are found when the cloud is not marginally bound, and also for the case of a cloud starting from rest. We also show how the strength of the naked singularity depends on the density and velocity distribution. Our analysis generalizes and simplifies the earlier work of Christodoulou and Newman [4,5] by dropping the assumption of evenness of density functions. It turns out that relaxing this assumption allows for a smooth transition from the naked singularity phase to the black-hole phase, and also allows for the occurrence of strong curvature naked singularities.Comment: 23 pages; Plain Tex; TIFR-TAP preprin