The Unified Field Equations and Schwarzschild's Solution. II.

1930 ◽  
Vol 35 (2) ◽  
pp. 214-214 ◽  
Author(s):  
Meyer Salkover
Keyword(s):  
Field Equations ◽  
Unified Field

On a non-symmetric theory of the pure gravitational field

1958 ◽  
Vol 54 (1) ◽  
pp. 72-80 ◽  
Author(s):  
D. W. Sciama
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Symmetric Tensor ◽  
Momentum Tensor ◽  
Unified Field Theory ◽  
Field Equations ◽  
Metric Tensor ◽  
Unified Field

ABSTRACTIt is suggested, on heuristic grounds, that the energy-momentum tensor of a material field with non-zero spin and non-zero rest-mass should be non-symmetric. The usual relationship between energy-momentum tensor and gravitational potential then implies that the latter should also be a non-symmetric tensor. This suggestion has nothing to do with unified field theory; it is concerned with the pure gravitational field.A theory of gravitation based on a non-symmetric potential is developed. Field equations are derived, and a study is made of Rosenfeld identities, Bianchi identities, angular momentum and the equations of motion of test particles. These latter equations represent the geodesics of a Riemannian space whose contravariant metric tensor is gij–, in agreement with a result of Lichnerowicz(9) on the bicharacteristics of the Einstein–Schrödinger field equations.

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 static spherically symmetric solutions in a unified field theory

1957 ◽  
Vol 53 (2) ◽  
pp. 489-493 ◽  
Author(s):  
John Moffat
Keyword(s):  
Charged Particle ◽  
Electric Energy ◽  
Gravitational Theory ◽  
Spherically Symmetric ◽  
Unified Field Theory ◽  
Field Equations ◽  
Schwarzschild Solution ◽  
Fundamental Properties ◽  
Unified Field ◽  
Conditions At Infinity

ABSTRACTA brief account is given of the fundamental properties of a new generalization ((1), (2)) of Einstein's gravitational theory. The field equations are then solved exactly for the case of a static spherically symmetric gravitational and electric field due to a charged particle at rest at the origin of the space-time coordinates. This solution provides information about the gravitational field produced by the electric energy surrounding a charged particle and yields the Coulomb potential field. The solution satisfies the required boundary conditions at infinity, and it reduces to the Schwarzschild solution of general relativity when the charge is zero.

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.

scholarly journals A Simplified Presentation of Einstein's Unified Field Equations

Nature ◽  
1930 ◽  
Vol 125 (3161) ◽  
pp. 813-813
Author(s):  
H. T. H. P.
Keyword(s):  
Field Equations ◽  
Unified Field

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.

A Simplified Presentation of Einstein's Unified Field Equations

1930 ◽  
Vol 15 (210) ◽  
pp. 274
Author(s):  
H. T. H. Piaggio ◽  
T. Levi-Civita ◽  
J. Dougall
Keyword(s):  
Field Equations ◽  
Unified Field
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