# Charged axially symmetric solution and energy in teleparallel theory equivalent to general relativity

#### Abstract

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 - q 2A2ξ4. 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. © 2006 Springer-Verlag.

*This paper has been withdrawn.*