Massless scalar field in Robertson-Walker space-time

Recently, exact spatially-homogeneous solutions have been found for a conformally invariant massless scalar fieldS(t) coupled to a Robertson-Walker geometry. We investigate extending these solutions to inhomogeneous scalar fieldsS(t, x ^l ). For an isotropic scalar fieldS(t, r) we find a solution satisfying three of the five field equations. If we use REDUCE, we show that the remaining equations forceS=S(t).     

Contested terrains: Cities and hinterlands in post-apartheid boundary delimitations

In South Africa attempts are being made to address the socio-spatial distortions of the apartheid era through a more equitable distribution of resources, and the re-drawing of municipal geographical boundaries. However, boundaries are not neutral geographic lines. Boundary changes are often associated with a redistribution of political power and resources. The aim of this paper is to analyse the effects of the contemporary territorial and administrative restructuring on urban dynamics in South Africa. More specifically, the focus is on how the process of territorial restructuring impacted on metropolitan areas as well as on secondary cities and their hinterlands. Examining and elucidating the manner in which various social, economic and political forces have manifested themselves in the process of boundary delimitation in a major metropolitan centre as well as adjacent rural areas is a central theme of this paper. There were considerable contestations over the delimitation of new local government boundaries. Affluent metro authorities like that in Durban were opposed to the spatial extension of their boundaries because of the costs of the providing services and infrastructure in the deprived margins. Similarly, there was concern that incorporation of rural areas will result in increased municipal service charges being imposed on these communities. Tensions were heightened between urban and rural regions because traditional leaders believed that their territorial jurisdiction and authority were being undermined. In other parts of the country, the merger of traditionally white and black fragments of secondary cities often resulted in many black locations continuing to be marginalized. There appears to be neither the political will nor the economic capacity to upgrade these zones of marginalized urban communities. While the Municipal Demarcation Board was largely successful in eliminating the political geography of apartheid at a macro- scale, this paper suggests that the greater challenge for government and policy makers is to reduce the socio-spatial and economic inequalities which appears to be still very high and perhaps increasing. This revised version was published online in July 2006 with corrections to the Cover Date.     

Charged isotropic model with conformal symmetry

We investigate the behaviour of a charged isotropic model with conformal symmetry. The relationship between the gravitational potentials arising from the conformal condition is used to generate a new class of exact solutions to the Einstein-Maxwell equations. A specific form of the electric field intensity and the metric potential is required to avoid a singularity at the centre. We can find simple elementary functions for the matter variables and the potentials with realistic profiles. The causality conditions, stability conditions and energy conditions are satisfied. Masses, radii, central densities and surface redshifts are generated, and the values are consistent with the compact stars 4U 1538-52 and PSR J1614-2230.     

Temperature evolution in the presence of anisotropic stresses

In a recent paper by Das et al. (Astrophys. Space Sci. 361:99, 2016) it was shown that the sign of the anisotropy parameter plays a pivotal role in determining the time of formation of the horizon of a collapsing radiating star. Spurred on by this observation we investigate the impact of the (an)isotropy featured in the (Das et al. in Astrophys. Space Sci. 361:99, 2016) collapsing model on the temperature profiles of the evolving system. We show that the temperature within the stellar interior is increased as the anisotropy in the pressure grows. Relaxational effects due to heat dissipation within the core further enhances the temperature at each interior point of the stellar distribution.     

Characteristics of surface ozone in Agra,a sub-urban site in Indo-Gangetic Plain

In the present study, measurements of surface ozone (\(\hbox {O}_{3}\)) and its precursors (NO and \(\hbox {NO}_{2}\)) were carried out at a sub-urban site of Agra (\(27{^{\circ }}10'\hbox {N}\), \(78{^{\circ }}05'\hbox {E}\)), India during May 2012–May 2013. During the study period, average concentrations of \(\hbox {O}_{3}\), NO, and \(\hbox {NO}_{2}\) were \(39.6 \pm 25.3\), \(0.8 \pm 0.8\) and \(9.1 \pm 6.6 \, \hbox {ppb}\), respectively. \(\hbox {O}_{3}\) showed distinct seasonal variation in peak value of diurnal variation: summer \({>}\) post-monsoon \({>}\) winter \({>}\) monsoon. However, \(\hbox {NO}_{2}\) showed highest levels in winter and lowest in monsoon. The average positive rate of change of \(\hbox {O}_{3}\) (08:00–11:00 hr) was highest in April (16.3 ppb/hr) and lowest in August (1.1 ppb/hr), while average negative rate of change of \(\hbox {O}_{3}\) (17:00–19:00 hr) was highest in December (–13.2 ppb/hr) and lowest in July (–1.1 ppb/hr). An attempt was made to identify the \(\hbox {VOC--NO}_{\mathrm{x}}\) sensitivity of the site using \(\hbox {O}_{3}/\hbox {HNO}_{3}\) ratio as photochemical indicator. Most of the days this ratio was above the threshold value (12–16), which suggests \(\hbox {NO}_{\mathrm{x}}\) sensitivity of the site. The episodic event of ozone was characterized through meteorological parameters and precursors concentration. Fine particles (\(\hbox {PM}_{2.5}\)) cause loss of ozone through heterogeneous reactions on their surface and reduction in solar radiation. In the study, statistical analyses were used to estimate the amount of ozone loss.     

Engineering-geological mapping of tropical soils for land-use planning and geotechnical purposes: A case study from Jamaica, West Indies

An area of a Tertiary and Cretaceous deposits, 100–310 m above sea level and on predominant 20–45°, highly dissected, concave slopes was investigated to assess its geotechnical characteristics and land use planning implications. Lithologies include turbidites, fluvial conglomerates, breccias, sandstones, mudrocks, carbonates, granodiorite, acid dykes, chloritized and epidotized volcanics, andesite and Holocene fluvial deposits. Bedrock is highly fractured and sheared, hydrothermally altered and highly weathered. Soils are quite variable, with a strong geological control on soil properties. Soils are generally sandy to gravely, with local silts and clays in mudrocks, within Holocene alluvium or in hydrothermally altered and sheared granodiorites. The soils are composed of 0.14–80.00% gravel; 5.36–62.50% sand, 2.33–50.55% silt, 0.17–51.50% clay, and total fine content between 2.50 and 94.50%, with natural moisture between 4 and 44% during the dry season, plastic limit between 6 and 35%, liquid limit between 19 and 83% and plasticity index between 1 and 59%. Sandy soils have residual friction angles between 19 and 39°, PI values less than 35% with cohesion between 1.00 and 5.27 KN/m² for cohesive samples. ASTM classification of soils include soil groups GC, GM, GW, GP, SP, SM, SC, SM, SC, ML, CL and CH.

Based on the characteristics of the terrain, the geotechnical and land use planning problems include high landslide frequency and susceptibility, soil erosion, fluvial and reservoir sedimentation, high debris flow hazard, cut slope failures, potentially expansive clays and silts, seepage erosion and soil piping, differential settlement in interlayered competent and incompetent lithologies, high solution erosion and potential subsidence over limestones, waste water disposal problems and groundwater pollution and seismic induced settlement and ground failures. These phenomena suggest that systematic site investigations should be conducted prior to the utilization of these areas for construction and development in order to minimize the deleterious effects resulting from ground failure.     

Charged compact objects in the linear regime

Astrophysical compact stars provide a natural laboratory for testing theoretical models which are otherwise difficult to prove from an experimental setup. In our present work we analyse an exact solution to the Einstein-Maxwell system for a charged anisotropic compact body in the linear regime. The charged parameter may be set to zero which gives us the case of neutral solutions. We have tuned the model parameters for the uncharged case so as to match with recent updated mass-radius estimates for five different compact objects. Then we make a systematic study of the effect of charge for the different parameter set that fits the observed stars. The effect of charge is clearly illustrated in the increase of mass. We show that the physical quantities for the objects PSR J1614-2230, PSR J1903+327, Vela X-1, SMC X-1, Cen X-3 are well behaved.     

Robertson-Walker-type universes with conformally-invariant scalar field

Recently, Innaiah and Reddy (1985) obtained a flat Robertson-Walker-type solution for the Einstein field equations with the trace-free energy-momentum tensor of a conformally invariant scalar field as source. Here we show that the field equations force the scalar field to be independent of time. Furthermore, we obtain open and closed Robertson-Walker-type solutions and observe that, once again, the scalar field has to be independent of time.     

On the scalar-tensor theory of Lau and Prokhovnik

Recently Lau & Prokhovnik (1986) have formulated a new scalar-tensor theory of gravitation which reconciles Dirac’s large numbers hypothesis with Einstein’s theory of general relativity. The present work points out an error in the time-dependent cosmological term and the scalar potential given by Lau and Prokhovnik. The correct forms for these quantities are derived. Further, a vacuum Robertson-Walker solution to the generalized field equations is obtained, under an anasatz that we propose, which illustrates that the theory is, in some sense, incomplete.