A class of exact isotropic solutions of Einstein’s equations and relativistic stellar models in general relativity

In this paper we have studied a particular class of exact solutions of Einstein’s gravitational field equations for spherically symmetric and static perfect fluid distribution in isotropic coordinates. The Schwarzschild compactness parameter, GM/c ² R, can attain the maximum value 0.1956 up to which the solution satisfies the elementary tests of physical relevance. The solution also found to have monotonic decreasing adiabatic sound speed from the centre to the boundary of the fluid sphere. A wide range of fluid spheres of different mass and radius for a given compactness is possible. The maximum mass of the fluid distribution is calculated by using stellar surface density as parameter. The values of different physical variables obtained for some potential strange star candidates like Her X-1, 4U 1538–52, LMC X-4, SAX J1808.4?3658 given by our analytical model demonstrate the astrophysical significance of our class of relativistic stellar models in the study of internal structure of compact star such as self-bound strange quark star.     

Two-Fluid Bianchi Type II Cosmological Models

In this paper we present a class of solutions of Einstein's field equations describing two-fluid models of the universe in a locally rotationally symmetric Bianchi type II space-time. In these models one fluid is the radiation distribution which represents the cosmic microwave background and the other fluid is the perfect fluid representing the matter content of the universe. It is found that both the fluids are comoving in the locally rotationally symmetric Bianchi type II space-time. The behaviour of the radiation density, matter density, the ratio of the matter density to the radiation density and the pressure has been discussed. A subclass of solutions is found to describe models of a spatially homogeneous and partially isotropic universe evolving from a radiation dominated era to a pressure free matter dominated era. This revised version was published online in July 2006 with corrections to the Cover Date.     

Relation between VLF phase deviations and solar X-ray fluxes during solar flares

Sudden phase anomalies (SPA's) observed in the phase of GBR 16 kHz VLF signals during the years 1977 to 1983 have been analysed in the light of their associated solar X-ray fluxes in the 0.5–4 Å and 1–8 Å bands. An attempt has been made to investigate the solar zenith angle () dependence of the integrated solar X-ray flux for producing SPA's. It is deduced from the observations for < 81° that the phase deviation increases linearly as a whole with increasing solar X-ray fluxes in these two bands. The threshold X-ray flux needed to produce a detectable SPA effect has been estimated to be 1.6 × 10^–4 ergcm^–2 s^–1 and 1.8 × 10^–3 ergcm^–2 s^–1 in the 0.5–4 Å and 1–8 Å bands, respectively. For both bands the average cross section for all atmospheric constituents at a height of 70 km is almost equal to the absorption cross section for the 3 Å X-ray emission.     

Limnological Studies in a Subtropical System (Lake Sattal,India)

A limnological study was carried out in the subtropical Lake Sattal (Kumaun Himalaya) during 1979. The lake was thermally stratified during warm months and a low percentage saturation of dissolved oxygen occurred in the bottom waters. Two maxima of phytoplankton occurred in the Eastern basin in contrast to only one in the Western basin. The peak in the latter developed more than a month (October) after the second peak in the former (August). Bacillariophyceae contributed highest in the Western basin (43.2%) whereas the Dinophyceae had the least share in the Eastern basin (8.0%). Most of the dominant phytoplankters were: Synedra ulna, Fragilaria, Gymnodinium, Crucigenia and Closteridium siamensis. Interestingly, blue-green alga Nostoc, dominated for some time in autumn. A total of 12 genera of rotifers, 6 genera of cladocerans and 1 genus of copepods were found in Lake Sattal basins. Dominant zooplankters included Keratella, Cyclops, Anuraeopsis, Polyarthra and Trichocerca, and there is a high ratio of rotifers to copepods and cladocerans. On comparing the averaged values of both the basins, the Eastern basin showed a 64% larger population of zooplankton than the Western basin. A comparison is made with the plankton of the other subtropical lake-systems of this region.     

Diversity, distribution pattern and conservation status of the plants used in liver diseases/ailments in Indian Himalayan Region

Introduction The Indian Himalayan Region (IHR) is known for its unique, natural, representative biodiversity (Samant et al. 1998a). This biodiversity is being utilized by the inhabitants of the IHR in various forms, i.e., medicine, food (wild edibles), fuel, fodder, timber, making agricultural tools, fiber, religious and various other purposes (Samant and Dhar 1997, Samant et al. 1998b). In the remote areas of the IHR where primary health centers are located far from the villages, the in…     

Well-behaved relativistic charged super-dense star models

A new class of charged super-dense star models is obtained by using an electric intensity, which involves a parameter, K. The metric describing the model shares its metric potential g ₄₄ with that of Durgapal’s fourth solution (J. Phys. A, Math. Gen. 15:2637, 1982). The pressure-free surface is kept at the density ρ _b =2×10¹⁴ g/cm³ and joins smoothly with the Reissner-Nordstrom solution. The charge analogues are well-behaved for a wide range, 0≤K≤59, with the optimum value of X=0.264 i.e. the pressure, density, pressure–density ratio and velocity of sound are monotonically decreasing and the electric intensity is monotonically increasing in nature for the given range of the parameter K. The maximum mass and the corresponding radius occupied by the neutral solution are 4.22M _Θ and 20 km, respectively for X=0.264. For the charged solution, the maximum mass and radius are defined by the expressions M≈(0.0059K+4.22)M _Θ and r _b ≈−0.021464K+20 km respectively.     

Well behaved class of charge analogue of Heintzmann’s relativistic exact solution

We present a well behaved class of Charge Analogue of Heintzmann (Z. Phys. 228:489, 1969) solution. This solution describes charge fluid balls with positively finite central pressure and positively finite central density ; their ratio is less than one and causality condition is obeyed at the centre. The outmarch of pressure, density, pressure-density ratio and the adiabatic speed of sound is monotonically decreasing, however, the electric intensity is monotonically increasing in nature. The solution gives us wide range of constant K (1.25≤K≤15) for which the solution is well behaved and therefore, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degrees of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³. Corresponding to K=1.25 and X=0.42, the maximum mass of the star comes out to be 3.64M _Θ with linear dimension 24.31 km and central redshift 1.5316.     

Variety of Well behaved parametric classes of relativistic charged fluid spheres in general relativity

The paper presents a variety of classes of interior solutions of Einstein–Maxwell field equations of general relativity for a static, spherically symmetric distribution of the charged fluid with well behaved nature. These classes of solutions describe perfect fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the center. The outmarch of pressure, density, pressure–density ratio and the adiabatic speed of sound is monotonically decreasing for these solutions. Keeping in view of well behaved nature of these solutions, two new classes of solutions are being studied extensively. Moreover, these classes of solutions give us wide range of constant K for which the solutions are well behaved hence, suitable for modeling of super dense star. For solution (I₁) the mass of a star is maximized with all degree of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³ corresponding to K=1.19 and X=0.20, the maximum mass of the star comes out to be 2.5M _Θ with linear dimension 25.29 Km and central redshift 0.2802. It has been observed that with the increase of charge parameter K, the mass of the star also increases. For n=4,5,6,7, the charged solutions are well behaved with their neutral counterparts however, for n=1,2,3, the charged solution are well behaved but their neutral counterparts are not well behaved.     

GPS-derived precipitable water vapour and its comparison with MODIS data for Almora, Central Himalaya, India

The present study is an attempt to analyse the precipitable water vapour (PWV) derived from Global Positioning System (GPS) and observed meteorological data over Almora, Central Himalayan Region. The PWV values derived using GPS study is compared with the corresponding moderate resolution imaging spectro-radiometer (MODIS) data. The statistical analysis reveals a positive correlation between both methods. Moderate resolution imaging spectroradiometer near-infrared (MODIS NIR) clear column water vapour product shows a higher correlation (R ² = 90–93 %) with GPS-derived precipitable water vapour on annual scale as compared to the seasonal scale (R ² = 62–87 %). MODIS is found to be overestimating in NIR clear column where the magnitude of bias and RMSE show systematic changes from season to season. Monsoon is an important phenomenon in the Indian weather context and holds significant importance in Central Himalayan ecosystem. The monthly and seasonal variation in precipitable water vapour is related with monsoon onset in the region. Diurnal variations in precipitable water vapour are studied with other meteorological data over Almora during dry and wet season. The precipitable water vapour had minimum value in the morning, increases in the afternoon to evening and again decreases to the midnight in both the dry and wet seasons. These results suggest that diurnal variation of water vapour is caused by the transport of water vapour by thermally induced local circulation.