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.

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

1931 ◽  
Vol 2 (3) ◽  
pp. 140-150 ◽  
Author(s):  
G. C. McVittie
Keyword(s):  
Field Theory ◽  
Axial Symmetry ◽  
Spherical Symmetry ◽  
Unified Field Theory ◽  
Field Equations ◽  
Mass Particle ◽  
Unified Field ◽  
Theory Of Gravitation ◽  
Axis Of Symmetry ◽  
Single Coordinate

Einstein has recently adopted a new set of field-equations in his Unified Field-Theory of Gravitation and Electricity, the so-called theory of parallelism at a distance or Teleparallelism, and has given a solution of these equations with spherical symmetry, corresponding to the field of a charged mass-particle. In the present paper we discuss the solution of these equations with axial symmetry, which corresponds to a statical field whose field-variables depend on a single coordinate only, viz. the coordinate which is measured along the axis of symmetry.

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)

The equations of motion in the non-symmetric unified field theory

1954 ◽  
Vol 226 (1166) ◽  
pp. 366-377 ◽  
Keyword(s):  
Equations Of Motion ◽  
Coulomb Force ◽  
Unified Field Theory ◽  
Field Equations ◽  
Original Theory ◽  
Unified Field ◽  
Theory Of Gravitation ◽  
The One ◽  
A Charge ◽  
Weak Fields

The field equations of the non-symmetric unified theory of gravitation and electromagnetism are changed so that they imply the existence of the Coulomb force between electric charges. It is shown that the equations of motion of charged masses then follow correctly to the order of approximation considered. The equations for weak fields in the modified theory are derived and shown to lead to Maxwell’s equations together with a restriction on the current density. This restriction is different from that in the original theory, and in the static, spherically symmetric case permits a charge distribution more likely to correspond to a particle. The failure of the original theory to lead to the equations of motion is related to the structure of the quantities appearing in it, and reasons are given for supposing that no nonsymmetric theory simpler than the one put forward is likely to give these equations in their conventional form.

A unified field theory of gravitation and electromagnetism

1953 ◽  
Vol 10 (3) ◽  
pp. 230-235 ◽  
Author(s):  
G. Stephenson ◽  
C. W. Kilmister
Keyword(s):  
Field Theory ◽  
Unified Field Theory ◽  
Unified Field ◽  
Theory Of Gravitation

The Kerr–Newman metric in the nonsymmetric unified field theory

1976 ◽  
Vol 54 (12) ◽  
pp. 1274-1276 ◽  
Author(s):  
D. H. Boal
Keyword(s):  
Field Theory ◽  
Electromagnetic Field ◽  
Charged Particle ◽  
Unified Field Theory ◽  
Maxwell Theory ◽  
Antisymmetric Part ◽  
Unified Field ◽  
Theory Of Gravitation

The method introduced by Newman and Janis for obtaining the metric of a rotating, charged particle in the Einstein–Maxwell theory of gravitation and electromagnetism is examined in the context of the nonsymmetric unified field theory. It is found that a transformation very similar to theirs, when applied to the antisymmetric part of the tensor gμv, will generate the required electromagnetic field associated with the Kerr–Newman metric.

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.

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