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
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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