An exact charged solution with axial symmetry is obtained in the teleparallel equivalent of general relativity (TEGR). The associated metric has the structure function $G(\xi)=1-{ \xi}^2-2mA{ \xi}^3-q^2A^2{ \xi}^4$. 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 factorisable form $(1-{ \xi}^2)(1+r_{ +}A\xi)(1+r_{ -}A\xi)$ with $r_{ \pm}$ as the horizons of Reissner-Nordstr$\ddot{ o}$m 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-Nordstr$\ddot{ o}$m 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.
Categories: gr-qc