scholarly journals A Field Theory with Curvature and Anticurvature

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
M. I. Wanas ◽  
Mona M. Kamal
Keyword(s):  
Field Theory ◽  
Free Space ◽  
Unified Field Theory ◽  
Field Equations ◽  
Weak Equivalence Principle ◽  
Unified Field ◽  
Special Cases ◽  
Geometric Objects ◽  
Pure Gravity ◽  
Physical Quantities

The present work is an attempt to construct a unified field theory in a space with curvature and anticurvature, the PAP-space. The theory is derived from an action principle and a Lagrangian density using a symmetric linear parameterized connection. Three different methods are used to explore physical contents of the theory obtained. Poisson’s equations for both material and charge distributions are obtained, as special cases, from the field equations of the theory. The theory is a pure geometric one in the sense that material distribution, charge distribution, gravitational and electromagnetic potentials, and other physical quantities are defined in terms of pure geometric objects of the structure used. In the case of pure gravity in free space, the spherical symmetric solution of the field equations gives the Schwarzschild exterior field. The weak equivalence principle is respected only in the case of pure gravity in free space; otherwise it is violated.

scholarly journals TELEPARALLEL LAGRANGE GEOMETRY AND A UNIFIED FIELD THEORY: LINEARIZATION OF THE FIELD EQUATIONS

2013 ◽  
Vol 10 (03) ◽  
pp. 1250092 ◽  
Author(s):  
M. I. WANAS ◽  
NABIL L. YOUSSEF ◽  
A. M. SID-AHMED
Keyword(s):  
Field Theory ◽  
Approximate Solution ◽  
Order Of Approximation ◽  
Unified Field Theory ◽  
Field Equations ◽  
First Order ◽  
Unified Field ◽  
Vertical Field ◽  
Geometric Objects ◽  
Linearized Theory

This paper is a natural continuation of our previous paper: "Teleparallel Lagrange geometry and a unified field theory, Class. Quantum Grav.27 (2010) 045005 (29 pp)". In this paper, we apply a linearization scheme on the field equations obtained in the above-mentioned paper. Three important results under the linearization assumption are accomplished. First, the vertical fundamental geometric objects of the EAP-space lose their dependence on the positional argument x. Secondly, our linearized theory in the Cartan-type case coincides with the GFT in the first-order of approximation. Finally, an approximate solution of the vertical field equations is obtained.

scholarly journals An Interpretation of the Field Tensor in the Unified Field Theory

1954 ◽  
Vol 7 (1) ◽  
pp. 1 ◽  
Author(s):  
NW Taylor
Keyword(s):  
Field Theory ◽  
Current Density ◽  
Free Space ◽  
Spherically Symmetric ◽  
Symmetric Part ◽  
Field Tensor ◽  
Unified Field Theory ◽  
Field Equations ◽  
Unified Field ◽  
Electric And Magnetic Fields

It is assumed that the skew symmetric part of the field tensor gik is a complex, self-dual tensor. This permits the whole set of field equations for free space to be derived directly from the theory without the introduction of an electric current density tensor. However, with this assumption it appears impossible for spherically symmetric electric and magnetic fields to exist in free space.

Unified Field Theory

1950 ◽  
Vol 2 ◽  
pp. 427-439 ◽  
Author(s):  
Max Wyman
Keyword(s):  
Field Theory ◽  
Variational Principle ◽  
Electromagnetic Fields ◽  
Linear Connection ◽  
Hamiltonian Function ◽  
Unified Theory ◽  
Unified Field Theory ◽  
Field Equations ◽  
Unified Field

Introduction. In a recent unified theory originated by Einstein and Straus [l], the gravitational and electromagnetic fields are represented by a single nonsymmetric tensor gy which is a function of four coordinates xr(r = 1, 2, 3, 4). In addition a non-symmetric linear connection Γjki is assumed for the space and a Hamiltonian function is defined in terms of gij and Γjki. By means of a variational principle in which the gij and Γjki are allowed to vary independently the field equations are obtained and can be written(0.1)(0.2)(0.3)(0.4)

scholarly journals Solution with Axial Symmetry of Einstein's Equations of Teleparallelism

1932 ◽  
Vol 3 (1) ◽  
pp. 37-45 ◽  
Author(s):  
J. D. Parsons
Keyword(s):  
Field Theory ◽  
General Solution ◽  
Axial Symmetry ◽  
Unified Field Theory ◽  
Einstein’S Equations ◽  
Field Equations ◽  
Einstein's Equations ◽  
Unified Field ◽  
Theory Of Gravitation

In a recent paper Dr G. C. McVittie discussed the solution with axial symmetry of Einstein's new field-equations in his Unified Field Theory of Gravitation and Electricity. Owing to an error in his calculation of the field equations, Dr McVittie did not obtain the general solution, which we discuss in the present paper.

The General Static Spherically Symmetric Solution of the "Weak" Unified Field Equations

1962 ◽  
Vol 14 ◽  
pp. 568-576 ◽  
Author(s):  
J. R. Vanstone
Keyword(s):  
Ricci Tensor ◽  
Spherically Symmetric ◽  
Dimensional Manifold ◽  
Unified Field Theory ◽  
Field Equations ◽  
Unified Field ◽  
Spherically Symmetric Solution ◽  
Geometric Objects ◽  
Symmetric Connection ◽  
Image Position

In 1947 Einstein and Strauss (2) proposed a unified field theory based on a four-dimensional manifold characterized by a nonsymmetric tensor gij and a non-symmetric connection , where(1)Using a variational principle in which gij and are independently varied, the above authors obtain the equivalent of the following field equations:(2a)(2b)In these equations a comma denotes partial differentiation with respect to the co-ordinates of the manifold, Wij is the Ricci tensor formed from and the notationfor the symmetric and skew-symmetric parts of geometric objects Q is employed.

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