2017/02/12 by Sumaira Saleem Akhtar, Tahir Hussain, Akhtar, Sumaira Saleem +5
Physics and Astronomy · #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Solar and Space Plasma Dynamics
paper · pdf · doi:10.48550/arxiv.1702.04637
openalex publication_date 2017/02/12 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28
Considering the degenerate and non-degenerate cases, we provide a complete\nclassification of static plane symmetric spacetimes according to conformal\nRicci collineations (CRCs) and conformal matter collineations (CMCs). In case\nof non-degenerate Ricci tensor, a general form of vector field generating CRCs\nis found in terms of unknown functions of t and x, subject to some\nintegrability conditions. The integrability conditions are then solved in\ndifferent cases depending upon the nature of Ricci tensor and it is concluded\nthat static plane symmetric spacetimes possess 7, 10 or 15-dimensional Lie\nalgebra of CRCs. Moreover, it is found that these spacetimes admit infinite\nnumber of CRCs when the Ricci tensor is degenerate. A similar procedure is\nadopted for the study of CMCs in degenerate and non-degenerate matter tensor\ncases. The exact form of some static plane symmetric spacetimes metrics is\nobtained admitting non-trivial CRCs and CMCs. Finally, we present some physical\nimplications of our obtained results by considering a perfect fluid as a source\nof the energy-momentum tensor.\n