Classification of non-conformally flat static plane symmetric perfect fluid solutions via proper conformal vector fields in f (T) gravity

The aim of this paper is to classify non-conformally flat static plane symmetric (SPS) perfect fluid solutions via proper conformal vector fields (CVFs) in f(T) gravity. For this purpose, first we explore some SPS perfect fluid solutions of the Einstein field equations (EFEs) in f(T) gravity. Second, we utilize these solutions to find proper CVFs. In this study, we found 16 cases. A detailed study of each case reveals that in three of these cases, the space-times admit proper CVFs whereas in the rest of the cases, either the space-times become conformally flat or they admit proper homothetic vector fields (HVFs) or Killing vector fields (KVFs). The dimension of CVFs for non-conformally flat space-times in f(T) gravity is four, five or six.