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 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 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.

scholarly journals KERR–NEWMAN SOLUTION AND ENERGY IN TELEPARALLEL EQUIVALENT OF EINSTEIN THEORY

2007 ◽  
Vol 22 (14) ◽  
pp. 1047-1056 ◽  
Author(s):  
GAMAL G. L. NASHED
Keyword(s):  
Black Hole ◽  
Vector Field ◽  
Symmetric Solution ◽  
Gravitational Energy ◽  
Rotation Parameter ◽  
Axially Symmetric ◽  
Einstein Theory ◽  
Newman Black Hole ◽  
Charge Parameter ◽  
Electromagnetic Vector Potential

An exact charged axially symmetric solution of the coupled gravitational and electromagnetic fields in the teleparallel equivalent of Einstein theory is derived. It is characterized by three parameters "the gravitational mass M, the charge parameter Q and the rotation parameter a" and its associated metric gives Kerr–Newman spacetime. The parallel vector field and the electromagnetic vector potential are axially symmetric. We then calculate the total energy using the gravitational energy–momentum. The energy is found to be shared by its interior as well as exterior. Switching off the charge parameter we find that no energy is shared by the exterior of the Kerr–Newman black hole.

scholarly journals The post - Newtonian rotation of Earth: a first approach

1988 ◽  
Vol 128 ◽  
pp. 341-347
Author(s):  
J. Schastok ◽  
M. Soffel ◽  
H. Ruder ◽  
M. Schneider
Keyword(s):  
Angular Momentum ◽  
Rotational Motion ◽  
Symmetric Model ◽  
Free Precession ◽  
Axially Symmetric ◽  
Relativistic Description ◽  
Theories Of Gravity ◽  
Momentum Complex ◽  
Tensor Of Inertia ◽  
Corotating Frame

The problems of dynamics of extended bodies in metric theories of gravity are reviewed. In a first approach towards the relativistic description of the Earth's rotational motion the post - Newtonian treatment of the free precession of a pseudo - rigid and axially symmetric model Earth is presented. Definitions of angular momentum, pseudo - rigidity, the corotating frame, tensor of inertia and axial symmetry of the rotating body are based upon the choice of the standard post - Newtonian (PN) coordinates and the full PN energy momentum complex. In this framework, the relation between angular momentum and angular (coordinate) velocity is obtained. Since the PN Euler equations for the angular velocity here formally take their usual Newtonian form it is concluded that apart from PN modifications (renormalizations) of the inertia tensor, the rotational motion of our pseudo - rigid and axially symmetric model Earth essentially is “Newtonian”.

Relativistic axially symmetric flows of a perfect fluid

1977 ◽  
Vol 355 (1680) ◽  
pp. 53-60 ◽  
Keyword(s):  
Angular Momentum ◽  
Perfect Fluid ◽  
Momentum Density ◽  
Dynamical Variable ◽  
Axially Symmetric ◽  
A Value ◽  
Maximum Value ◽  
Spherical Vortex ◽  
Fluid Particles ◽  
The Moment

We consider axially symmetric stationary relativistic flows of a perfect fluid which is characterized by a general density-pressure relation µ ( p ). It is shown that the meridional components of velocity can be derived from a stream-function, the trajectories of the fluid particles being spirals wound around torus-shaped surfaces. The moment of the velocity, and another dynamical variable, are conserved for fluid particles along their motion. However, the relativistic angular-momentum-density is convectively conserved only in a fluid in which the velocity of sound equals the velocity of light. We evaluate the total angular momentum L and the total energy E of a spherical vortex in such a fluid, based on a solution given previously. Putting L = 1/2ℏ and E = mc 2 , where m denotes the mass of the neutron, and letting the maximum value of the flow in the vortex equal c , we get a value of 1.2 x 10 -13 cm for the radius of the vortex.

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