Open Access Original Research Article

Extension Rules of Newman–Janis Algorithm for Rotation Metrics in General Relativity

Yu-Ching, Chou

Physical Science International Journal, Page 1-14
DOI: 10.9734/psij/2020/v24i630194

Aims: The aim of this study is to extend the formula of Newman–Janis algorithm (NJA) and introduce the rules of the complexifying seed metric. The extension of NJA can help determine more generalized axisymmetric solutions in general relativity.
Methodology: We perform the extended NJA in two parts: the tensor structure and the seed metric function. Regarding the tensor structure, there are two prescriptions, the Newman–Penrose null tetrad and the Giampieri prescription. Both are mathematically equivalent; however, the latter is more concise. Regarding the seed metric function, we propose the extended rules of a complex transformation by r2/Σ and combine the mass, charge, and cosmologic constant into a polynomial function of r.

Results: We obtain a family of axisymmetric exact solutions to Einstein’s field equations, including the Kerr metric, Kerr–Newman metric, rotating–de Sitter, rotating Hayward metric, Kerr–de Sitter metric and Kerr–Newman–de Sitter metric. All the above solutions are embedded in ellipsoid- symmetric spacetime, and the energy-momentum tensors of all the above metrics satisfy the energy conservation equations.

Conclusion: The extension rules of the NJA in this research avoid ambiguity during complexifying the transformation and successfully generate a family of axisymmetric exact solutions to Einsteins field equations in general relativity, which deserves further study.

Open Access Original Research Article

Study of Naturally Occurring Radioactive Materials and Some Heavy Metals from Intake of Some Nuts and Seeds in South-Western, Nigeria

Augustine Kolapo Ademola, Ruth Omoseeke Morakinyo

Physical Science International Journal, Page 15-23
DOI: 10.9734/psij/2020/v24i630195

The concentration of NORMs and some toxic heavy metals in some nuts and seeds commonly consumed in the south-western states of Nigeria were investigated. The analysis was done with NaI(TI) spectrometry and Inductively Coupled Plasma (ICP) respectively. The concentration of 226Ra, 232Th, and 40K in the samples was found to be below the world average. The mean values are 6.6±1.8, 3.6±1.0 and 98.2±13.5 Bq/kg, in nuts and 8.4±2.6, 2.6±1.3 and 97.6±15.0 Bq/kg in seeds respectively. The effective dose in nuts was calculated to be 13.99 and 12.0 µSv in seeds. The fatal and hereditary cancer risk estimated from the consumption of the nuts and seeds are lower than 1.0 x 10-6 which is the lowest limit. Concentration of metals in the samples descend as Fe > Zn > Cu > Cr. The Hazard Indices of heavy metals are lower than 1 except for in Cocoa which is higher than 1 due to the high concentration of Cu and Fe. Therefore, the nuts and seeds analyzed in this study are contaminated with Cu and Fe and so must be taken with care so that consumers will not be exposed to excessive concentration of these metals which may have undesirable effects.

Open Access Original Research Article

Unsaturated Stream-Aquifer Connection When the Riverbed Itself Desaturates

Hubert J. Morel- Seytoux

Physical Science International Journal, Page 24-33
DOI: 10.9734/psij/2020/v24i630196

In a previous series of 3 articles in this Journal we have looked at the situation when the aquifer desaturates while the riverbed (clogging layer) remained saturated.  However it is quite possible that the riverbed itself will desaturate, particularly if the river stage is low and especially when the river goes dry. In this article we look at the situation when indeed the riverbed desaturates as the capillary pressure at the interface between the bottom of the riverbed and the top of the unsaturated zone in the aquifer exceeds the riverbed entry pressure, while the river itself does not go dry. Utilizing different soil textures for a riverbed we found that the seepage rate, following a slight increase in value, tends rapidly to an asymptotic limit which is not much higher than the seepage value at incipient desaturation of the riverbed.

Thus the assumption that the riverbed does not desaturate may lead to grossly exaggerated values of the seepage rate.

Open Access Original Research Article

On the Synergic Relationships between Special Relativity and Quantum Theories

E. Comay

Physical Science International Journal, Page 34-43
DOI: 10.9734/psij/2020/v24i630197

The successful results of the relativistic form of a quantum field theory that is derived from aLagrangian density justify its general usage. The significance of the Euler-Lagrange equations of a quantum particle is analysed. Many advantages of this approach, like abiding by the conservation laws of energy, momentum, angular momentum, and charge are well known. The merits of this approach also include other properties that are still not well known. For example, it is shown that a quantum function of the form ψ(t, r) describes a pointlike particle. Furthermore, the Lagrangian density and the Hamiltonian density take a different relativistic form – the Lagrangian density is a Lorentz scalar, whereas the Hamiltonian density is the T00 component of the energy-momentum tensor. It is proved that inconsistencies in the electroweak theory stem from negligence of the latter point.

Open Access Original Research Article

Heliospheric Modulation of GCR at Mid and High Latitudes

Kingsley Chukwudi Okpala, Darlene Florence Kalu, Nnaemeka Onyekachi Njoku- Achu

Physical Science International Journal, Page 44-55
DOI: 10.9734/psij/2020/v24i630198

The variations of Galactic Cosmic Ray (GCR) as compared with the behaviour of various solar activity indices, heliospheric parameters and the geomagnetic index Ap during 1999-2015, which covers part of cycles 23 and cycle 24 have been studied.  Two sets of data were considered, consisting respectively of all days of the month and the five quietest days. Neutron Monitor Stations of Moscow and Rome (mid latitude stations) and Inuvik and Oulu (High latitude stations) were employed. Cosmic Ray (CR) wave characteristics were obtained by the harmonics method.  The mean, diurnal amplitude of the first, second, and third harmonics were calculated and profiled. Furthermore, correlation analysis was carried out to determine the association between parameters. Results showed that the total magnetic field BT and the sunspot number (SSN) showed the strongest association with CR in both quiet conditions and all day conditions considered. The higher harmonics showed a slightly stronger association with CR than lower harmonics. A time-lag of about 12-15 months was observed for SSN suggesting a potential for predicting CR flux, while the total magnetic field had a zero lag for all the heliospheric parameters considered.