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

G. G.L. Nashed, Ain Shams University

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.