Browsing by Author "Kahil M.E."

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An AP structure with Finslerian Flavor: Path equations
(Maik Nauka Publishing / Springer SBM, 2016) Wanas M.I.; Kahil M.E.; Kamal M.M.; Astronomy Department; Faculty of Science; Cairo University; Giza; Egypt; Egyptian Relativity Group (ERG); Cairo; Egypt; The American University in Cairo; New Cairo; Egypt; October University for Modern Sciences and Arts; Giza; Egypt; Mathematics Department; Faculty of Girls; Ain Shams University; Cairo; Egypt
The Bazanski approach to deriving paths is applied to Finsler geometry. The approach is generalized and applied to a new developed geometry called �Absolute parallelism with Finslerian Flavor� (FAP). A set of path equations is derived for the FAP. It is a horizontal (h) set. A striking feature in this set is that the coefficient of the torsion term jumps by a step of one-half from one equation to the other. It is tempting to believe that the h-set admits some quantum features. Comparisons with the corresponding sets in other geometries are given. Conditions for reducing the set of path equations obtained to well-known path equations in some geometries are summarized in a schematic diagram. � 2016, Pleiades Publishing, Ltd.
Dark Matter: the Problem of Motion
(Pleiades Publishing, 2019) Kahil M.E.; Faculty of Engineering; Modern Sciences and Arts University; Giza; Egypt; Egyptian Relativity Group; Cairo; Egypt
Dark matter (DM) may be studied through the motion of objects following nongeodesic trajectories either due to the existence of an extra mass as a projection of higher dimensions onto lower ones or as motion of dipolar particles and fluids in the halos of spiral galaxies. The effect of DM has been extended nearby the core of the galaxy by means of the excess of mass appearing in the motion of fluids in the accretion disc. Nongeodesic equations and those of their deviation are derived in the presence of different classes of bimetric theories of gravity. The stability of these trajectories using the geodesic deviation technique is investigated. � 2019, Pleiades Publishing, Ltd.
Is dark matter an extra-dimensional effect?
(2009) Kahil M.E.; Harko T.; Mathematics Department; Modern Sciences and Arts University; Cairo; Egypt; Department of Physics; Center for Theoretical and Computational Physics; University of Hong Kong; Pok Fu Lam Road; Hong Kong; Hong Kong
We investigate the possibility that the observed behavior of test particles outside galaxies, which is usually explained by assuming the presence of dark matter, is the result of the dynamical evolution of particles in higher dimensional spacetimes. Hence, dark matter may be a direct consequence of the presence of an extra force, generated by the presence of extra dimensions, which modifies the dynamic law of motion, but does not change the intrinsic properties of the particles, like, for example, the mass (inertia). We discuss in some detail several possible particular forms for the extra force, and the acceleration law of the particles is derived. Therefore, the constancy of the galactic rotation curves may be considered as an empirical evidence for the existence of the extra dimensions. � 2009 World Scientific Publishing Company.
Motion in bimetric type theories of gravity
(Maik Nauka Publishing / Springer SBM, 2017) Kahil M.E.; October University for Modern Sciences and Arts; Giza; Egypt; Egyptian Relativity Group; Cairo; Egypt
The problem of motion of different test particles, charged and spinning objects with a constant spin tensor in different versions of the bimetric theory of gravity is considered by deriving their corresponding path and path deviation equations using a modified Bazanski Lagrangian. Such a Lagrangian, as in the framework of Riemannian geometry, has a capability to obtain path and path deviations of any object simultaneously. This method enables us to derive the path and path deviation equations of different objects orbiting in very strong gravitational fields. 2017, Pleiades Publishing, Ltd.
Motion in brane world models: The Bazanski approach
(2007) Kahil M.E.; Mathematics Department; Modern Sciences and Arts University; Giza; Egypt
Recently, path equations have been obtained for charged and spinning objects in brane world models, using a modified Bazanski Lagrangian. In this study, path deviation equations of extended objects are derived. The significance of moving extended objects in brane world models is examined. Motion in non-symmetric brane world models is also considered. � 2007 American Institute of Physics.
Motion in Kaluza-Klein type theories
(2006) Kahil M.E.; Mathematics Department; Modern Sciences and Arts University; Giza; Egypt; Mathematics Department; American University in Cairo; Cairo; Egypt
Path and path deviation equations for charged, spinning and spinning charged objects in different versions of Kaluza-Klein (KK) theory using a modified Bazanski Lagrangian have been derived. The significance of motion in five dimensions, especially for a charged spinning object, has been examined. We have also extended the modified Bazanski approach to derive the path and path deviation equations of a test particle in a version of non-symmetric KK theory. 2006 American Institute of Physics.
Path and path deviation equations for p-branes
(2012) Pavi, M.; Kahil M.E.; Joef Stefen Institute; Ljubljana; Slovenia; October University For Modern Sciences and Arts; Giza; Egypt; The American University in Cairo; New Cairo; Egypt
Path and path deviation equations for neutral, charged, spinning and spinning charged test particles, using a modified Bazanski Lagrangian, are derived. We extend this approach to strings and branes. We show how the Bazanski Lagrangian for charged point particles and charged branes arises la Kaluza-Klein from the Bazanski Lagrangian in 5-dimensions. 2012 Versita Warsaw and Springer-Verlag Wien.
Path and path deviation equations in Kaluza-Klein type theories: A brief introduction
(2008) Kahil M.E.; Mathematics Department; Modern Sciences and Arts University; Giza; Egypt; Mathematics Department; The American University in Cairo; Cairo; Egypt
The problem of motion in higher dimensions is an intriguing problem. This can be seen by studing path and path deviation equations for charged, spinning and spinning charged objects in higher dimensions. The significance of motion in higher dimensions may yield some physical implications on the effect of the extra dimension on the current motion. In this approach, we apply the Bazanski method to derive path and path deviation equations for different objects in five dimensions. � 2008 Springer-Verlag Berlin Heidelberg.
Population dynamics: A geometrical approach of some epidemic models
(2011) Kahil M.E.; Modern Sciences and Arts University; Giza; Egypt; American University in Cairo; New Cairo; Egypt
Recently, the behavior of different epidemic models and their relation both to different types of ge- ometries and to some biological models has been revisited. Path equations representing the behavior of epidemic models and their corresponding deviation vectors are examined. A comparison between paths and their deviation vectors in Riemannian and Finslerian Geometries is presented.
Spinning and Spinning Deviation Equations for Special Types of Gauge Theories of Gravity
(IEEE Computer Society, 2018) Kahil M.E.; Modern Sciences and Arts University; Giza; Egypt; Egyptian Relativity Group; Cairo; Egypt
The problem of spinning and spin deviation equations for particles as defined by their microscopic effect has led many authors to revisit non-Riemannian geometry describing torsion and its relation with the spin of elementary particles. We obtain a new method for detecting the existence of torsion by deriving the equations of spin deviations in different classes of non-Riemannian geometries, using a modified Baz anski method. We find that the translational and rotational gauge potentials regulate the spin deviation equation in the framework of the Poincare gauge field theory of gravity. 2018, Pleiades Publishing, Ltd.