scholarly journals ENERGY AND ANGULAR MOMENTUM OF GENERAL FOUR-DIMENSIONAL STATIONARY AXI-SYMMETRIC SPACE–TIME IN TELEPARALLEL GEOMETRY

2008 ◽  
Vol 23 (12) ◽  
pp. 1903-1918 ◽  
Author(s):  
GAMAL G. L. NASHED
Keyword(s):  
Angular Momentum ◽  
Symmetric Space ◽  
Electromagnetic Fields ◽  
Momentum Distribution ◽  
Symmetric Solution ◽  
Space Time ◽  
Theory Of Gravitation ◽  
Momentum Complex ◽  
Tetrad Theory

We derive an exact general axi-symmetric solution of the coupled gravitational and electromagnetic fields in the tetrad theory of gravitation. The solution is characterized by four parameters: M (mass), Q (charge), a (rotation) and L (NUT). We then calculate the total exterior energy using the energy–momentum complex given by Møller in the framework of Weitzenböck geometry. We show that the energy contained in a sphere is shared by its interior as well as exterior. We also calculate the components of the spatial momentum to evaluate the angular momentum distribution. We show that the only nonvanishing components of the angular momentum is in the Z direction.

scholarly journals CHARGED AXIALLY SYMMETRIC SOLUTION, ENERGY AND ANGULAR MOMENTUM IN TETRAD THEORY OF GRAVITATION

2006 ◽  
Vol 21 (15) ◽  
pp. 3181-3197 ◽  
Author(s):  
GAMAL G. L. NASHED
Keyword(s):  
Angular Momentum ◽  
Symmetric Solution ◽  
Vector Fields ◽  
Momentum Density ◽  
Relativity Theory ◽  
Axially Symmetric ◽  
Theory Of Gravitation ◽  
Charge Parameter ◽  
Momentum Complex ◽  
Tetrad Theory

Charged axially symmetric solution of the coupled gravitational and electromagnetic fields in the tetrad theory of gravitation is derived. The metric associated with this solution is an axially symmetric metric which is characterized by three parameters "the gravitational mass M, the charge parameter Q and the rotation parameter a." The parallel vector fields and the electromagnetic vector potential are axially symmetric. We calculate the total exterior energy. The energy–momentum complex given by Møller in the framework of the Weitzenböck geometry "characterized by vanishing the curvature tensor constructed from the connection of this geometry" has been used. This energy–momentum complex is considered as a better definition for calculation of energy and momentum than those of general relativity theory. The energy contained in a sphere is found to be consistent with pervious results which is shared by its interior and exterior. Switching off the charge parameter, one finds that no energy is shared by the exterior of the charged axially symmetric solution. The components of the momentum density are also calculated and used to evaluate the angular momentum distribution. We found no angular momentum contributes to the exterior of the charged axially symmetric solution if zero charge parameter is used.

scholarly journals Energy-momentum complex in M�ller's tetrad theory of gravitation

1993 ◽  
Vol 32 (9) ◽  
pp. 1627-1642 ◽  
Author(s):  
F. I. Mikhail ◽  
M. I. Wanas ◽  
Ahmed Hindawi ◽  
E. I. Lashin
Keyword(s):  
Theory Of Gravitation ◽  
Momentum Complex ◽  
Tetrad Theory

scholarly journals REISSNER–NORDSTRÖM SPACE–TIME IN THE TETRAD THEORY OF GRAVITATION

2007 ◽  
Vol 16 (01) ◽  
pp. 65-79 ◽  
Author(s):  
GAMAL G. L. NASHED ◽  
TAKESHI SHIRAFUJI
Keyword(s):  
Exact Solutions ◽  
Arbitrary Function ◽  
Energy Content ◽  
Analytic Solutions ◽  
Spherically Symmetric ◽  
Theory Of Gravitation ◽  
Momentum Complex ◽  
Charged Source ◽  
Superpotential Method ◽  
Tetrad Theory

We give two classes of spherically symmetric exact solutions of the coupled gravitational and electromagnetic fields with charged source in the tetrad theory of gravitation. The first solution depends on an arbitrary function H(R,t). The second solution depends on a constant parameter η. These solutions reproduce the same metric, i.e. the Reissner–Nordström metric. If the arbitrary function which characterizes the first solution and the arbitrary constant of the second solution are set to be zero, then the two exact solutions will coincide with each other. We then calculate the energy content associated with these analytic solutions using the superpotential method. In particular, we examine whether these solutions meet the condition, which Møller required for a consistent energy–momentum complex, namely, we check whether the total four-momentum of an isolated system behaves as a four-vector under Lorentz transformations. It is then found that the arbitrary function should decrease faster than [Formula: see text] for R → ∞. It is also shown that the second exact solution meets the Møller's condition.

Impossibility of class one electromagnetic fields

1969 ◽  
Vol 66 (1) ◽  
pp. 153-154 ◽  
Author(s):  
S. N. Pandey ◽  
I. D. Kansal
Keyword(s):  
Symmetric Space ◽  
Electromagnetic Fields ◽  
Spherical Symmetry ◽  
Space Time ◽  
Spherically Symmetric

In a recent paper (1) it has been established that a spherically symmetric space-time of class one cannot describe an electromagnetic distribution of energy. In this investigation the inconsistency of class one conditions with Rainich algebraic conditions was shown in case of spherical symmetry. In the present paper it is shown that the result is true for space-time of class one, in general.

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