arXiv subjects
Publications and source records attributed to F. I. Mikhail.
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.
The field equations of the new general relativity (NGR) have been applied to an absolute parallelism space having three unknown functions of the radial coordinate. The field equations have been solved using two different schemes. In the first scheme, we used the conventional procedure used in orthodox general relativity. In the second scheme, we examined the effect of signature change. The latter scheme gives a solution which is different from the Schwarzschild one. In both methods we find solution of the field equations under the same constraint imposed on the parameters of the theory. We also calculated the energy associated with the solutions in the two cases using the superpotential method. We found that the energetic content of one of the solutions is different from that of the other. A comparison between the two solutions obtained in the present work and a third one obtained by Hayashi and Shirafuji (1979) shows that the change of the signature may give rise to new physics.
The field equations of the generalized field theory (GFT) are derived from an action principle. A comparison between (GFT), Møller's tetrad theory of gravitation (MTT), and general relativity is carried out regarding the Lagrangian of each theory. The results of solutions of the field equations, of each theory, are compared in case of spherical symmetry. The differences between the results are discussed and interpreted.
The field equations of the new general relativity constructed by Hayashi and Shirafuji (1979), have been applied to two different geometric structures, given by Robertson (1932), in the domain of cosmology. In the first application a family of models, involving two of the parameters characterizing the field equations of the new general relativity, is obtained. In the second application the models obtained are found to involve one parameter only. The cosmological parameters in both applications are calculated and some cosmological problems are discussed in comparison with the corresponding results of other field theories.
Møller's Tetrad Theory of Gravitation is examined with regard to the energy-momentum complex. The energy-momentum complex as well as the superpotential associated with Møller's theory are derived. Møller's field equations are solved in the case of spherical symmetry. Two different solutions, giving rise to the same metric, are obtained. The energy associated with one solution is found to be twice the energy associated with the other. Some suggestions to get out of this inconsistency are discussed at the end of the paper.
The general solution of Møller's field equations in case of spherical symmetry is derived. The previously obtained solutions are verified as special cases of the general solution.