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Five-dimensional teleparallel theory equivalent to general relativity,the axially symmetric solution,energy and spatial momentum

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Chinese Physics B 2011年第11期20卷 102-109页

作者： gamal G.L.Nashed mathematics Department Faculty of ScienceAin Shams University

A theory of （4＋1）-dimensional gravity is developed on the basis of the teleparallel theory equivalent to general relativity. The fundamental gravitational field variables are the five-dimensional vector fields （pentad）, defined globally on a manifold m, and gravity is attributed to the torsion. The Lagrangian density is quadratic in the torsion tensor. We then give the exact five-dimensional solution. The solution is a generalization of the familiar Schwarzschild and Kerr solutions of the four-dimensional teleparallel equivalent of general relativity. We also use the definition of the gravitational energy to calculate the energy and the spatial momentum.

关键词： five-dimensional teleparallel equivalent of general relativity five-dimensional solution energy and spatial momentum

Cosmological application on five-dimensional teleparallel theory equivalent to general relativity

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Chinese Physics B 2012年第10期21卷 122-129页

作者： gamal G.L.Nashed mathematics Department Faculty of ScienceKing Faisal UniversityP.O.Box 380 Al-Ahsaa 31982the Kingdom of Saudi Arabia mathematics Department Faculty of ScienceAin Shams UniversityCairo 11566Egypt Center for Theoretical Physics British University of EgyptSherouk City 11837P.O.Box 43Egypt

A theory of（4＋1）-dimensional gravity has been developed on the basis of which equivalent to the theory of general relativity by *** fundamental gravitational field variables are the 5-dimensional（5D） vector fields（pentad）,defined globally on a manifold m,and gravity is attributed to the *** Lagrangian density is quadratic in the torsion *** then apply the field equations to two different homogenous and isotropic geometric structures which give the same line element,i.e.,FRW in five *** cosmological parameters are calculated and some cosmological problems are discussed.

关键词： 5D teleparallel equivalent of general relativity 5D solutions cosmological parameters cosmological problems

Gravitational collapse with standard and dark energy in the teleparallel equivalent of general relativity

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Chinese Physics B 2012年第6期21卷 57-62页

作者： gamal G.L.Nashed mathematics Department Faculty of ScienceKing Faisal UniversityP.O.Box 380 Al-Ahsaa 31982the Kingdom of Saudi Arabia mathematics Department Faculty of ScienceAin Shams UniversityCairo11566Egypt Center for Theoretical Physics British University of EgyptSherouk City 11837P.O.Box 43Egypt

A perfect fluid with self-similarity of the second kind is studied within the framework of the teleparallel equivalent of general relativity （TEGR）. A spacetime which is not asymptotically fiat is derived. The energy conditions of this spacetime are studied. It is shown that after some time the strong energy condition is not enough to satisfy showing a transition from standard matter to dark energy. The singularities of this solution are discussed.

关键词： perfect fluid with self-similarity of second kind teleparallel equivalent of general relativ-ity asymptotically nonflat spacetime energy conditions

Kumaraswamy Inverted Topp–Leone Distribution with Applications to COVID-19 Data

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Computers, materials & Continua 2021年第7期68卷 337-358页

作者： Amal S.Hassan Ehab m.Almetwally gamal m.Ibrahim Faculty of Graduate Studies for Statistical Research Cairo UniversityGiza12613Egypt Faculty of Business Administration Delta University of Science and TechnologyMansoura35511Egypt High Institute for management Sciences Belqas35511Egypt

In this paper, an attempt is made to discover the distributionof COVID-19 spread in different countries such as;Saudi Arabia, Italy,Argentina and Angola by specifying an optimal statistical distribution for analyzing the mortality rate of COVID-19. A new generalization of the recentlyinverted Topp Leone distribution, called Kumaraswamy inverted Topp–Leonedistribution, is proposed by combining the Kumaraswamy-G family and theinverted Topp–Leone distribution. We initially provide a linear representationof its density function. We give some of its structure properties, such as quantile function, median, moments, incomplete moments, Lorenz and Bonferronicurves, entropies measures and stress-strength reliability. Then, Bayesian andmaximum likelihood estimators for parameters of the Kumaraswamy invertedTopp–Leone distribution under Type-II censored sample are *** estimator is regarded using symmetric and asymmetric loss functions. As analytical solution is too hard, behaviours of estimates have beendone viz monte Carlo simulation study and some reasonable comparisonshave been presented. The outcomes of the simulation study confirmed theefficiencies of obtained estimates as well as yielded the superiority of Bayesianestimate under adequate priors compared to the maximum likelihood *** to COVID-19 in some countries showed that the new distributionis more appropriate than some other competitive models.

关键词： Kumaraswamy-G family maximum likelihood Bayesian method COVID-19 moments quantile function stress-strength reliability

Regular Charged Solutions in mφller＇s Tetrad Theory of Gravitation

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Chinese Physics Letters 2007年第11期24卷 3059-3062页

作者： gamal G. L. Nashed Department of mathematics Faculty of Science Ain Shams University Cairo Egypt

We find the most general tetrads which give a regular charged spacetime in tetrad theory of gravitation. The metric is a static one and it includes the Schwarzschild and Fteissner Nordstrom black holes. The energy content contained in a sphere of radius R is calculated using the superpotential given by mφller in the context of Weitzenbock spacetime.

关键词： Regular Charged Solutions Tetrad Gravitation

mΦller＇s Energy of Kerr-NUT metric

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Chinese Physics Letters 2008年第4期25卷 1202-1204页

作者： gamal G. L. Nashed mathematics Department Faculty of Science Ain Shams University Cairo Egypt

The energy distribution of the Kerr-NUT （Newman-Unti-Tamburino） spacetime is calculated using mΦller＇s energy-momentum complex within the framework of the Riemannian geometry.

关键词： TETRAD THEORY NEWmAN SPACETImE QUASILOCAL mASS LOCALIZATION GRAVITATION COmPLEX

Cylindrically Symmetric Solution in Teleparallel Theory

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Chinese Physics Letters 2010年第10期27卷 30-33页

作者： gamal G. L. Nashed Centre for Theoretical Physics The British University in Egypt E1-Sherouk City Misr-Ismalia Desert Road Postal No 11837 PO Box 43 Egypt mathematics Department Faculty of Science Ain Shams University Cairo Egypt

The field equations of a special class of teleparallel theory of gravitation and electromagnetic fields are applied to tetrad space having cylindrical symmetry with four unknown functions of radial coordinate r and azimuth angle θ. The vacuum stress-energy momentum tensor with one assumption concerning its specific form generates one non-trivial exact analytic solution. This solution is characterized by a constant magnetic field parameter B0. If B0 = 0, then the solution will reduce to the flat spacetime. The energy content is calculated using the superpotential given by mФller in the framework of teleparallel geometry. The energy contained in a sphere is found to be different from the pervious results.

关键词： Fields Ficus religiosa Solutions Solutes Energy

Cosmological applications in Kaluza-Klein theory

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Chinese Physics B 2012年第4期21卷 631-637页

作者： m. I. Wanas gamal G. L. Nashed A. A. Nowaya Astronomy Department Faculty of Science Cairo University Giza Egypt mathematics Department Faculty of Science Ain Shams University Cairo 11566 Egypt Center for Theoretical Physics British University of Egypt Sherouk City 11837 P.O. Box 43 Egypt mathematics Department Faculty of Science King Faisal University P.O. Box 380 Al-Ahsaa 31982 the Kingdom of Saudi Arabia Egyptian Relativity Group (ERG) Physics Department Faculty of Science Monofia University Monofia Egypt

The field equations of Kaluz-Klein （KK） theory have been applied in the domain of cosmology. These equations are solved for a fiat universe by taking the gravitational and the cosmological constants as a function of time t. We use Taylor＇s expansion of cosmological function, A（t）, up to the first order of the time t. The cosmological parameters are calculated and some cosmological problems are discussed.

关键词： Kaluz-Klein theory cosmology Taylor's expansion of cosmological function

Preliminary rib support requirements for solid coal ribs using a coal pillar rib rating(CPRR)

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International Journal of mining Science and Technology 2021年第1期31卷 15-22页

作者： Khaled mohamed mark Van Dyke gamal Rashed morgan mSears Robert Kimutis National Institute for Occupational Safety and Health Pittsburgh Mining Research DivisionPittsburghPA 15236USA

Researchers from the National Institute for Occupational Safety and Health(NIOSH)are developing a coal pillar rib rating(CPRR)technique to measure the integrity of coal *** CPRR characterizes the rib composition and evaluates its impact on the inherent stability of the coal *** CPRR utilizes four parameters:rib homogeneity,bedding condition,face cleat orientation with respect to entry direction,and rib *** these parameters are measurable in the field.A rib data collecting procedure and a simple sheet to calculate the CPRR were *** developed CPRR can be used as a rib quality mapping tool in underground coal mines and to determine the potential of local rib instabilities and support requirements associated with overburden *** calculations were conducted for 22 surveyed solid coal ribs,mainly composed of coal *** on this study,the rib performance was classified into four categories.A preliminary minimum primary rib support density(PRSD)line was obtained from these surveyed *** sample cases are presented that illustrate the data collection form and CPRR calculations.

关键词： Coal rib stability Rib support design Coal pillar rib rating Rib quality mapping CPRR Coal classification