Eur. Phys. J. C (2007) 49: 851-857
https://doi.org/10.1140/epjc/s10052-006-0154-x

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

^* e-mail: nashed652001@yahoo.com

Received: 7 August 2006
Revised: 8 October 2006
Published online: 2 December 2006

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-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.