The Relativistic Generalization of the Gravitational Force for Arbitrary Spacetimes

It has been suggested that re-expressing relativity in terms of forces could provide fresh insights. The formalism developed for this purpose only applied to static, or conformally static, space-times. Here we extend it to arbitrary space-times. It is hoped that this formalism may lead to a workable definition of mass and energy in relativity.Comment: 16 page

Weyl collineations that are not curvature collineations

Though the Weyl tensor is a linear combination of the curvature tensor, Ricci tensor and Ricci scalar, it does not have all and only the Lie symmetries of these tensors since it is possible, in principle, that "asymmetries cancel". Here we investigate if, when and how the symmetries can be different. It is found that we can obtain a metric with a finite dimensional Lie algebra of Weyl symmetries that properly contains the Lie algebra of curvature symmetries. There is no example found for the converse requirement. It is speculated that there may be a fundamental reason for this lack of "duality".Comment: 9 page

Similarities Between Classical Timelike Geodesics in a Naked Reissner-Nordstrom Singularity Background and the Behaviour of Electrons in Quantum Theory

It is generally assumed that naked singularities must be physically excluded, as they could otherwise introduce unpredictable influences in their future null cones. Considering geodesics for a naked Reissner-Nordstrom singularity, it is found that the singularity is effectively clothed by its repulsive nature. Regarding electron as naked singularity, the size of the clothed singularity (electron) turns out to be classical electro-magnetic radius of the electron, to an observer falling freely from infinity, initially at rest. The size shrinks for an observer falling freely from infinity, with a positive initial velocity. For geodetic parameters corresponding to negative energy there are trapped geodesics. The similarity of this picture with that arising in the Quantum Theory is discussed.Comment: 8 pages, 6 figure

Assessment of Nutritional Status and Its Determinants Among Students of Army Public School, Okara, Pakistan

Background: Malnutrition is a health problem affecting growth and development of young children. Children under 15 years of age are the main victims of malnutrition. Malnutrition is attributed to a series of diverse etiological factors. Objective: To determine the nutritional status of the children of various age groups of school going children of Army Public School and to find out the association of socio-demographic variables and dietary habits with nutritional status. Methodology: It was a descriptive cross-sectional study conducted at Army Public School, Okara. Sample was selected through non-probability consecutive sampling. Duration of study was 6 months (Dec 2017 to May 2018). The study was conducted after getting formal approval from Institutional Ethical Review Board AFPGMI. The children were randomly selected for study from the enrollment register available in the principal's office. Participation in the study was voluntary with guaranteed confidentiality. The participants were given full right to quit study without mentioning reason at any time during data collection. After ruling out the exclusion criteria, 500 children fulfilling inclusion criteria were selected for study. An informed written consent was obtained from all selected children and their parents to take part in the study. Data for the assessment of nutritional status was obtained using anthropometry, biochemical laboratory test and eating habits / food preferences of the children. Results: In our study, mean age of children included in the study was 9.58±1.72 years. Out of 500 children, 252 (50.2%) were male while 248 (49.8%) female. The mean height of children was 134.88±11.69 cm. The mean weight of children was 30.25±8.47 kg. The mean OFC of children was 51.43±1.75 cm. Out of total 500 children, 85 (17%) were having BMI less than 18.5, 338 (67.6%) were having BMI within 18.5–24.9 while 77 (15.4%) children having BMI within 25-29.9. None of child was observed with BMI of ≥30. Among 85 children with below normal BMI, 63 had mild malnutrition (BMI between 17-18.4), 19 had moderate malnutrition (BMI 16-16.9) while 3 had severe malnutrition (BMI < 16) Conclusion: Malnutrition is a significant public health problem among preschool and school going children. And improving socio-economic condition along with literacy of mothers and preventing infections through personal hygiene might help in improving the nutritional status of children

Uniqueness of Flat Spherically Symmetric Spacelike Hypersurfaces Admitted by Spherically Symmetric Static Spactimes

It is known that spherically symmetric static spacetimes admit a foliation by {\deg}at hypersurfaces. Such foliations have explicitly been constructed for some spacetimes, using different approaches, but none of them have proved or even discussed the uniqueness of these foliations. The issue of uniqueness becomes more important due to suitability of {\deg}at foliations for studying black hole physics. Here {\deg}at spherically symmetric spacelike hy- persurfaces are obtained by a direct method. It is found that spherically symmetric static spacetimes admit {\deg}at spherically symmetric hypersurfaces, and that these hypersurfaces are unique up to translation under the time- like Killing vector. This result guarantees the uniqueness of {\deg}at spherically symmetric foliations for such spacetimes.Comment: 10 page

Foliation of the Kottler-Schwarzschild-De Sitter Spacetime by Flat Spacelike Hypersurfaces

There exist Kruskal like coordinates for the Reissner-Nordstrom (RN) black hole spacetime which are regular at coordinate singularities. Non existence of such coordinates for the extreme RN black hole spacetime has already been shown. Also the Carter coordinates available for the extreme case are not manifestly regular at the coordinate singularity, therefore, a numerical procedure was developed to obtain free fall geodesics and flat foliation for the extreme RN black hole spacetime. The Kottler-Schwarzschild-de Sitter (KSSdS) spacetime geometry is similar to the RN geometry in the sense that, like the RN case, there exist non-singular coordinates when there are two distinct coordinate singularities. There are no manifestly regular coordinates for the extreme KSSdS case. In this paper foliation of all the cases of the KSSdS spacetime by flat spacelike hypersurfaces is obtained by introducing a non-singular time coordinate.Comment: 12 pages, 4 figure

Spherically Symmetric Gravitational Collapse

In this paper, we discuss gravitational collapse of spherically symmetric spacetimes. We derive a general formalism by taking two arbitrary spherically symmetric spacetimes with $g_{00}=1$. Israel's junction conditions are used to develop this formalism. The formulae for extrinsic curvature tensor are obtained. The general form of the surface energy-momentum tensor depending on extrinsic curvature tensor components is derived. This leads us to the surface energy density and the tangential pressure. The formalism is applied to two known spherically symmetric spacetimes. The results obtained show the regions for the collapse and expansion of the shell.Comment: 12 pages, 4 figures, accepted for publication in Mod. Phys. Lett.

Fenologi, Morfologi, dan Hasil Empat Aksesi Kacang Bambara (Vigna Subterranea (L.) Verdc.)

Characterization and evaluation of genetic potential of bambara groundnut accessions is very important in order to obtain accessions with high yield potential and early maturity. The objective of this research was to study the phenology, morphology, and yield of four bambara groundnut accessions. This experiment was conducted using a randomized completely block design with one factor i.e. origin of accessions (Bogor and Sukabumi black testa, Sumedang black and brown testa). The results showed that days to seedling emergence of Sumedang brown testa were 9.7 days after sowing (DAS), three other accessions ranged from 8.0 to 8.3 DAS. Days to 75% flowering of Sumedang brown testa was 45.3 days, the other three accessions ranged from 46.0 to 46.7 DAS. Days to pod formation of Bogor and Sumedang accessions with black testa were 49 DAS, Sumedang brown testa at 50 DAS, and Sukabumi accession at 54 DAS. Physiological seed maturity of Bogor and Sukabumi accessions at 112 DAS, Sumedang brown testa at 116 DAS and black testa at 128 DAS. Morphological variation of four bambara groundnut accessions included color of plumule, petiole, seed coat (testa), and leaf shape. Accessions of Sukabumi and Bogor black testa were potential to be developed further because of its showing higher number and weight of pods, and earlier maturity compared to those of Sumedang accessions with black and brown testa