Axially symmetric solution in Teleparallel Theory of Gravitation

Abstract

An exact solution has an axial symmetry is obtained in the teleparallel theory of gravitation. The associated metric has the structure function G(xi)=1-xi^2-2mA(xi)^3. The cubic nature of the structure function can make calculations cumbersome. Using a coordinate transformation we get a tetrad that its associated metric has the structure function in a factorisable form. This new form has the advantage that its roots are now trivial to write down. The singularities of the obtained tetrad are studied. Using another coordinate transformation we get a tetrad that its associated metric gives the Schwarzschild spacetime. Calculate the energy content of this tetrad we get a meaningless result!