Conformal Killing symmetries of plane-symmetric static spacetimes in teleparallel theory of gravitation

This paper explores conformal Killing vectors in teleparallel theory for the plane-symmetric static spacetime. Ten non-linear coupled teleparallel conformal Killing equations are solved to get the general form of teleparallel conformal Killing vectors and the conformal factor along with the integrability conditions. Three different possibilities are considered where the spacetime may exhibit a teleparallel conformal Killing vector. In two cases the integrability conditions are solved completely and teleparallel conformal Killing vectors are obtained along with the conformal factor for the special choice of metric functions. Another possibility reveals that no teleparallel proper conformal Killing vector exists and the spacetime admits only a teleparallel homothetic vector.