Teleparallel Homothetic Symmetry of Special Axially Symmetric Static Spacetime
In this paper we are interested to find teleparallel proper homothetic vector fields over the Lorentzian manifold of special axially symmetric static spacetime. For the purpose we applied teleparallel Lie derivative to the metric for homothetic equations and obtained ten coupled non linear differential equations. These equations are then solved for each possibility of the metric functions and it comes out that only in one case teleparallel proper homothetic vector fields exist for the special choice of metric functions. The spacetime admit eight dimensional teleparallel homothetic vector fields in which one is proper teleparallel homothetic vector and remaining seven are teleparallel Killing vector fields
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