scholarly journals NON-MINIMAL RβF2-COUPLED ELECTROMAGNETIC FIELDS TO GRAVITY AND STATIC, SPHERICALLY SYMMETRIC SOLUTIONS

2011 ◽  
Vol 26 (20) ◽  
pp. 1487-1494 ◽  
Author(s):  
TEKIN DERELI ◽  
ÖZCAN SERT
Keyword(s):  
Variational Principle ◽  
Electromagnetic Fields ◽  
Lagrange Multipliers ◽  
Spherically Symmetric ◽  
Field Equations ◽  
First Order ◽  
Spherically Symmetric Solutions ◽  
Method Of Lagrange Multipliers ◽  
Electrically Charged ◽  
Static Spherically Symmetric Solutions

We investigate non-minimal RβF2-type couplings of electromagnetic fields to gravity. We derive the field equations by a first-order variational principle using the method of Lagrange multipliers. Then we present various static, spherically symmetric solutions describing the exterior fields in the vicinity of electrically charged massive bodies.

The general static spherically symmetric solution in Einstein’s unified field theory

1952 ◽  
Vol 210 (1102) ◽  
pp. 427-434 ◽  
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Spherically Symmetric ◽  
Unified Field Theory ◽  
Singular Surfaces ◽  
Field Equations ◽  
Unified Field ◽  
Spherically Symmetric Solution ◽  
Spherically Symmetric Solutions ◽  
Static Spherically Symmetric Solutions

The static spherically symmetric solutions of Einstein’s unified field equations previously given refer to an electric field alone or to a magnetic field alone. The general solutions in the case where both types of field exist together are now derived. After appropriate boundary conditions have been applied, the solutions may be interpreted to represent a magnetic field arising from a point pole, and an electric field arising from a dispersed charge distribution, but tending asymptotically to that of a point charge. The solutions have an infinity of singular surfaces, contain no arbitrary constant corresponding to the mass of the system, and in them the charge distributions contain both positive and negative electricity at different places. It appears that the only static spherically symmetric solutions likely to have any physical significance are certain of those referring to an electric field alone.

scholarly journals FERMIONS IN THE BACKGROUND OF DILATONIC SPHALERONS

1994 ◽  
Vol 09 (40) ◽  
pp. 3731-3739 ◽  
Author(s):  
GEORGE LAVRELASHVILI
Keyword(s):  
Gauge Field ◽  
Field Potential ◽  
Spherically Symmetric ◽  
Yang Mills ◽  
Zero Modes ◽  
Discrete Sequence ◽  
Number Of Zeros ◽  
Spherically Symmetric Solutions ◽  
Static Spherically Symmetric Solutions

We discuss the properties and interpretation of a discrete sequence of a static spherically symmetric solutions of the Yang-Mills dilaton theory. This sequence is parametrized by the number of zeros, n, of a component of the gauge field potential. It is demonstrated that solutions with odd n possess all the properties of the sphaleron. It is shown that there are normalizable fermion zero modes in the background of these solutions. The question of instability is critically analyzed.

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)

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