Cylindrically Symmetric Solution in Teleparallel Theory of Gravitation

Abstract

The field equations of a special class of teleparallel theory of gravitation and electromagnetic fields have been applied to tetrad space having cylindrical symmetry with four unknown functions of radial coordinate $r$ and azimuth angle $θ$. The vacuum stress-energy momentum tensor with one assumption concerning its specific form generates one non-trivial exact analytic solution. This solution is characterized by a constant magnetic field parameter $B_0$. If $B_0=0$ then, the solution will reduces to the flat spacetime. The energy content is calculated using the superpotential given in the framework of teleparallel geometry. The energy contained in a sphere is found to be different from the pervious results.