Conformal Collineations of the Ricci and Energy-Momentum Tensors in Static Plane Symmetric Spacetimes

摘要

Considering the degenerate and non-degenerate cases, we provide a completeclassification of static plane symmetric spacetimes according to conformalRicci collineations (CRCs) and conformal matter collineations (CMCs). In caseof non-degenerate Ricci tensor, a general form of vector field generating CRCsis found in terms of unknown functions of t and x, subject to someintegrability conditions. The integrability conditions are then solved indifferent cases depending upon the nature of Ricci tensor and it is concludedthat static plane symmetric spacetimes possess 7, 10 or 15-dimensional Liealgebra of CRCs. Moreover, it is found that these spacetimes admit infinitenumber of CRCs when the Ricci tensor is degenerate. A similar procedure isadopted for the study of CMCs in degenerate and non-degenerate matter tensorcases. The exact form of some static plane symmetric spacetimes metrics isobtained admitting non-trivial CRCs and CMCs. Finally, we present some physicalimplications of our obtained results by considering a perfect fluid as a sourceof the energy-momentum tensor.