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- Title
Conformal Collineations of the Ricci and Energy-Momentum Tensors in Static Plane Symmetric Space-Times.
- Authors
Akhtar, S. S.; Hussain, T.; Bokhari, A. H.; Khan, F.
- Abstract
We provide a complete classification of static plane symmetric space-times according to conformal Ricci collineations (CRCs) and conformal matter collineations (CMCs) in both the degenerate and nondegenerate cases. In the case of a nondegenerate Ricci tensor, we find a general form of the vector field generating CRCs in terms of unknown functions of t and x subject to some integrability conditions. We then solve the integrability conditions in different cases depending upon the nature of the Ricci tensor and conclude that the static plane symmetric space-times have a 7-, 10- or 15-dimensional Lie algebra of CRCs. Moreover, we find that these space-times admit an infinite number of CRCs if the Ricci tensor is degenerate. We use a similar procedure to study CMCs in the case of a degenerate or nondegenerate matter tensor. We obtain the exact form of some static plane symmetric space-time metrics that admit nontrivial CRCs and CMCs. Finally, we present some physical applications of our obtained results by considering a perfect fluid as a source of the energy-momentum tensor.
- Subjects
RICCI flow; CONFORMAL coatings; ENERGY momentum relationship; RELATIVISTIC energy; LIE algebras
- Publication
Theoretical & Mathematical Physics, 2018, Vol 195, Issue 1, p595
- ISSN
0040-5779
- Publication type
Article
- DOI
10.1134/S0040577918040116