Killing Symmetry in Special Axially Symmetric Static Spacetimes in Teleparalel Theory of Gravitation

In this paper we are searching for teleparallel Killing vector fields of special axially symmetric static spacetimes in teleparallel theory of gravitation by using direct integration and algebraic techniques. After thorough investigations, the whole problem is divided into three cases under different constraints. Two of the said cases give contradiction, while one of them gives the solution of the system comprising the killing equations in the form of killing vector fields. The dimension of the killing symmetry in this case is 10.