https://doi.org/10.1140/epjc/s10052-006-0154-x
Regular Article - Theoretical Physics
Charged axially symmetric solution and energy in teleparallel theory equivalent to general relativity
Mathematics Department, Faculty of Science, Ain Shams University, Cairo, Egypt
* e-mail: nashed652001@yahoo.com
Received:
7
August
2006
Revised:
8
October
2006
Published online:
2
December
2006
An exact charged solution with axial symmetry is obtained in the teleparallel equivalent of general relativity. The associated metric has the structure function G(ξ)=1-ξ2-2mAξ3-q2A2ξ4. The fourth order nature of the structure function can make calculations cumbersome. Using a coordinate transformation we get a tetrad whose metric has the structure function in a factorizable form (1-ξ2)(1+r+Aξ)(1+r-Aξ) with r± as the horizons of Reissner–Nordström space-time. This new form has the advantage that its roots are now trivial to write down. Then, we study the singularities of this space-time. Using another coordinate transformation, we obtain a tetrad field. Its associated metric yields the Reissner–Nordström black hole. In calculating the energy content of this tetrad field using the gravitational energy-momentum, we find that the resulting form depends on the radial coordinate! Using the regularized expression of the gravitational energy-momentum in the teleparallel equivalent of general relativity we get a consistent value for the energy.
© Springer-Verlag Berlin Heidelberg, 2007