Axially Symmetric-dS Solution in Teleparallel f(T) Gravity Theories

Abstract

We apply a tetrad field with six unknown functions to Einstein field equations. Exact vacuum solution, which represents axially symmetric-dS spacetime, is derived. We multiply the tetrad field of the derived solution by a local Lorentz transformation which involves a generalization of the angle ϕ and get a new tetrad field. Using this tetrad, we get a differential equation from the scalar torsion T=TαμνSαμν. Solving this differential equation we obtain a solution to the f(T) gravity theories under certain conditions on the form of f(T) and its first derivatives. Finally, we calculate the scalars of Riemann Christoffel tensor, Ricci tensor, Ricci scalar, torsion tensor, and its contraction to explain the singularities associated with this solution.