M. I. Wanas

A self-consistent world model

The field equations of the generalized field theory constructed by Mikhail and Wanas have been applied to a well-established geometrical structure given earlier by H. P. Robertson in connection with the cosmological problem. A unique solution, representing a specified expanding Universe (withq0=0, Ω0=0.75,k=−1) has been obtained. The model obtained has been compared with cosmological observations and with FRW-models of relativistic cosmology. It has been shown that the suggested model is free of particle horizons. The existence of singularities has been discussed.The two cases, when the associated Riemannian-space has a definite or indefinite metric are considered. The case of indefinite metric with signature (+ − − −) is found to be characterized byk=−1, while the case of +ve definite metric is characterized byk=+1. Apart from that difference, the two cases give rise to the same cosmological parameters. It has been shown that energy conditions are satisfied by the material contents in both cases.

Motion of Spinning Particles in Gravitational Fields

A new path equation in absolute parallelism (AP) geometry is derived. The equation is a generalization of three path equations derived in a previous work. It can be considered as a geodesic equation modified by a torsion term, whose numerical coefficient jumps by steps of one half. The torsion term is parametrized using the fine structure constant. It is suggested that the new equation may describe the trajectories of spinning particles under the influence of a gravitational field, and the torsion term represents a type of interaction between the quantum spin of the moving particle and the background field. Weak field limits of the new path equation show that the gravitational potential felt by a spinning particle is different from that felt by a spinless particle (or a macroscopic body). As a byproduct, and in order to derive the new path equation, the AP-space is reconstructed using a new affine connexion preserving metricity. The new AP-structure has non-vanishing curvature. In certain limits, the new AP-structure can be reduced either to the ordinary Riemannian space, or to the conventional AP-space.A new path equation in absolute parallelism (AP) geometry is derived. The equation is a generalization of three path equations derived in a previous work. It can be considered as a geodesic equation modified by a torsion term, whose numerical coefficient jumps by steps of one half. The torsion term is parametrized using the fine structure constant. It is suggested that the new equation may describe the trajectories of spinning particles under the influence of a gravitational field, and the torsion term represents a type of interaction between the quantum spin of the moving particle and the background field. Weak field limits of the new path equation show that the gravitational potential felt by a spinning particle is different from that felt by a spinless particle (or a macroscopic body). As a byproduct, and in order to derive the new path equation, the AP-space is reconstructed using a new affine connexion preserving metricity. The new AP-structure has non-vanishing curvature. In certain limits, the new AP-structure can be reduced either to the ordinary Riemannian space, or to the conventional AP-space.

Geometrical structures for cosmological applications

A set of conditions for selecting geometrical structures appropriate for cosmological applications is suggested. These conditions are being applied to two geometrical structures constructed mainly for cosmological applications. The algebraic manipulation language REDUCE 2 has been used to carry out the relevant calculations. Without the help of a computer, the calculations involved are very tedious. The results obtained show that one of the two structures should be ruled out as a model for cosmological applications. The combination of the results of the present paper and those of a previous one support the procedure known as ‘The Type Analysis’.

Quantum Features of Non-Symmetric Geometries

Paths in an appropriate geometry are usuallyused as trajectories of test particles in geometrictheories of gravity. It is shown that non-symmetricgeometries possess some interesting quantum features. Without carrying out any quantization schemes,paths in such geometries are naturally quantized. Twodifferent non-symmetric geometries are examined forthese features. It is proved that, whatever thenon-symmetric geometry is, we always get the same quantumfeatures. It is shown that these features appear only inthe pure torsion term (the anti-symmetric part of theaffine connection) of the path equations. The vanishing of the torsion leads to the disappearance ofthese features, regardless of the symmetric part of theconnection. It is suggested that, in order to beconsistent with the results of experiments andobservations, torsion term in path equations should beparametrized using an appropriate parameter.

New path equations in absolute parallelism geometry

The Bazanski approach, for deriving the geodesic equations in Riemannian geometry, is generalized in the absolute parallelism geometry. As a consequence of this generalization three path equations are obtained. A striking feature in the derived equations is the appearence of a torsion term with a numerical coefficients that jumps by a step of one half from equation to another. This is tempting to speculate that the paths in absolute parallelism geometry might admit a quantum feature.

Theoretical interpretation of cosmic magnetic fields

The paper discusses the possibilty of interpreting the magnetic fields of astronomical bodies in the framework of a unified field theory.Using one of the solutions of the generalized field theory, a direct relation between the polar magnetic field, the angular velocity and the gravitational potential of the body considered, is obtained. The geometric model used for applications has spherical symmetry and is of the type (FIGI).The predictions of the theoretical formula, obtained from the model, are compared with available observational data, and with the empirical formula of Blackett. The theoretical formula gives a possible interpretation of a seed magnetic field which will develop and produce the large-scale magnetic field observed for celestial objects. The formula shows that the field is generated as a result of rotation of a massive object.

Two notes about spin in absolute parallelism spaces

Two notes concerning the description of spin phenomena in curved spaces are given. The first note shows that absolute parallelism condition is necessary for the description of the dynamics of an electron in a gravitational field. The second one indicates that a class of gravity theories, including macroscopic spin, is not viable in absolute parallelism spaces.

Notes on applications of general relativity in free space : implication from the motion of a test particle

The equations of motion of a neutral test particle in the field obtained by Wanas (1990) are completely solved. The solution obtained is compared with corresponding solutions in the cases of the Reissner-Nordstrom field, the Kerr field, and the Kerr-Newman field. The comparison shows that the new constant, appeared in the field considered, is connected to electromagnetism and not to spin phenomena.

Cosmological applications in Kaluza-Klein theory

The field equations of Kaluza—Klein (KK) theory have been applied in the domain of cosmology. These equations are solved for a flat universe by taking the gravitational and the cosmological constants as a function of time t. We use Taylors expansion of cosmological function, Λ(t), up to the first order of the time t. The cosmological parameters are calculated and some cosmological problems are discussed.

Application of Theorems on Null-Geodesics on The Solar Limb Effect

A direct and more general calculation of the limb effect connected with red-shift observations is obtained. Result agrees completely, in its general form, with that obtained from observations of the solar spectra but with different value for the maximum effect.