Analysis of Einstein Field Equations of Static Plane Symmetric Space-Time in General Relativity via Lie Approach

Abstract

In this study, Einstein field equations of static plane symmetric space-time is discussed by means of Lie approach. Lie point symmetries are computed for the considered equations. Moreover, one dimensional conjugacy classes for symmetry algebra are reported. Additionally, similarity variables are derived which are further utilized to find the solutions for parameters $A$ and $B$ of the considered space-time. Both linearly independent and dependent relationships between the unknown parameters $A$ and $B$ are observed for different cases. At the end, some well-known solutions are presented.