Two Lagrangian functions are used to construct geometric field theories. One of these Lagrangians depends on the curvature of space, while the other depends on curvature and torsion. It is shown that the theory constructed from the first Lagrangian gives rise to pure gravity, while the theory constructed using the second Lagrangian gives rise to both gravity and electromagnetism. The two theories are constructed in a version of absolute parallelism geometry in which both curvature and torsion are, simultaneously, nonvanishing. One single geometric object, W-tensor, reflecting the properties of curvature and torsion, is defined in this version and is used to construct the second theory. The main conclusion is that a necessary condition for geometric representation of electromagnetism is the presence of a nonvanishing torsion in the geometry used.
Abstract:The present work represents a step in dealing with stellar structure using a pure geometric approach. Geometric field theory is used to construct a model for a spherically symmetric configuration. In this case, two solutions have been obtained for the field equations. The first represents an interior solution which may be considered as a pure geometric one in the sense that the tensor describing the material distributions is not a phenomenological object, but a part of the geometric structure used. A general equation of state for a perfect fluid, is obtained from, and not imposed on, the model. The second solution gives rise to Schwarzschild exterior field in its isotropic form. The two solutions are matched, at a certain boundary, to evaluate the constants of integration. The interior solution obtained shows that there are different zones characterizing the configuration: a central radiation dominant zone, a probable convection zone as a physical interpretation of the singularity of the model, and a corona like zone. The model may represent a type of main sequence stars. The present work shows that Einstein's geometerization scheme can be extended to gain more physical information within material distribution, with some advantages.Keywords: stellar structure • geometric field theories • main sequence stars • absolute parallelism geometry © Versita sp. z o.o.
Finsler geometry is a natural extension of the Riemannian geometry and a good a platform used to interpret the infrastructure of physical phenomena, especially for relativistic applications. Accordingly it is worthy to study spinning fluids in the context of this geometry that would share their benefits in cosmological applications. Equations of motion of spinning fluids and their corresponding deviation equations are obtained. The problem of motion for studying a fluid with a variable mass is also obtained. The set of Equations of spinning fluids and spinning deviation fluids equations for some classes of the Finslerian geometry have been derived, using a modified type of the Bazanski Lagrangian. Due to the richness of the Finslerian geometry, a new perspective for revisiting the problem of stability is based on solving the deviation equations of spinning fluids in strong fields of gravity is performed. Such a problem has a direct application on examining the stability of accretion disk orbiting Sgr A*.
The General theory of relativity is one of the most successful theories of gravity. Despite its successful applications, it has some difficulties in examining the behaviour of particles precisely in strong gravitational fields. Bi-metric type theories of gravity are classified as alternative theories of gravity that describing such strong gravitational fields, such as the gravitational field formed at the core of our galaxy. In order to obtain the equations of motion for spinning fluids, we use the Weyssenhoff tensor to express the spin fluid. The equations of motion for spinning fluids are derived using Euler-Lagrange equation. We present the equations of motion for spinning fluids and their corresponding spin deviation equations in some classes of Bi-metric type theories. Also, we obtain equations of motion for spinning fluids and their corresponding spin deviation for a variable mass. Moreover, we extend our study to examine the status of motion for spinning charged fluids and their corresponding spin deviation equations.
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