Charged Axially Symmetric Solution and Energy in Teleparallel Theory Equivalent to General Relativity

Understand

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.