Conformal symmetry analysis of complexity-free, plane-symmetric anisotropic configuration

We analyze the plane-symmetric configuration of the anisotropic distribution of matter regarding the vanishing complexity factor conditions. The Darmois junction conditions for interior as well as exterior hypersurfaces have been specified. We impose certain limitations on the junction conditions to identify the noteworthy outcomes. The formulation of the scalar functions for planar symmetry and how they relate to the fluid’s physical variables are discussed. The conformal killing vector is a significant restriction for obtaining accurate solutions for the field equations. The symmetries have been identified via a conformal Killing vector which provides the ability to figure out the coordinates that restrict a specific amount of independent parameters. We look into four families of conformal Killing vector solutions, some revealing dust presence and others satisfying the junction conditions.