Some anisotropic and perfect fluid plane symmetric solutions of Einstein's field equations using killing symmetries

Abstract The Einstein’s field equations (EFEs), central to the theory of general relativity, often require spacetime symmetries such as those defined by Killing vector fields to simplify their solutions and derive physically meaningful results. Killing vector fields preserve the metric of spacetime and yield vital conservation laws. This article presents a comprehensive study of Killing vector fields in the background of nonstatic plane symmetric spacetime using a novel method, the Rif tree approach. Using a Maple algorithm, this approach provides conditions on the metric coefficients that lead to additional Killing vector fields than the minimum ones. A detailed analysis yields a variety of spacetime metrics that admit different dimensional Killing algebras. The physical implications of the obtained metrics are discussed by finding the associated energy-momentum tensors. Several metrics are found to describe physically realistic models, including anisotropic and perfect fluid solutions of EFEs.