Lie Symmetries and Classification of Plane Symmetric Static Space-Times

In this study, we provide the Lie symmetries and a classification of plane symmetric static space-times. Based on the invariance of the Lagrange equations of plane symmetries static space-time systems under the transformation Lie group, we provide the Lie symmetry determination equation, Lie symmetry theorem, and the conserved quantity of the systems; by utilizing the Lie symmetry method to solute the system, we give complete classification of the plane symmetric static space-times systems. The research results indicate that using the Lie symmetry method to study plane symmetric static spacetime can identify a series of conserved quantities that exist in the system; Discovered 5 basic Lie symmetries in the system; When the metric parameters of the system are appropriately selected, the plane symmetric static spacetime can have 6, 7, 8, 9, 11, and 17 Lie symmetric symmetries and conserved quantities.