Complete Classification of Conformal Killing Symmetries of Plane-Symmetric Static Spacetimes in Teleparallel Theory

摘要

We have studied the conformal, homothetic and Killing vectors in the context of teleparallel theory of gravitation for plane-symmetric static spacetimes. We have solved completely the non-linear coupled teleparallel conformal Killing equations. This yields the general form of teleparallel conformal vectors along with the conformal factor for all possible cases of metric functions. We have found four solutions which are divided into one Killing symmetries and three conformal Killing symmetries. One of these teleparalel conformal vectors depends on x only and other is a function of all spacetime coordinates. The three conformal Killing symmetries contain three proper homothetic symmetries where the conformal factor is an arbitrary non-zero constant.