Curvature and Weyl collineations of Bianchi type V spacetimes |
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| Authors: | U. Camci I. Hussain Y. Kucukakca |
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| Affiliation: | aDepartment of Physics, Art and Science Faculty, Akdeniz University, 07058 Antalya, Turkey;bCenter for Advanced Mathematics and Physics, Campus of the College of Electrical and Mechanical Engineering, National University of Sciences and Technology, Rawalpindi, Pakistan;cDepartment of Physics, Art and Science Faculty, Çanakkale Onsekiz Mart University, 17100 Çanakkale, Turkey |
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| Abstract: | The objective of this paper is twofold: (a) First the curvature collineations of the Bianchi type V spacetimes are studied using rank argument of curvature matrix. It is found that the rank of the 6×6 curvature matrix is 3, 4, 5 or 6 for these spacetimes. In one of the rank 3 cases the Bianchi type V spacetime admits proper curvature collineations which form infinite dimensional Lie algebra. (b) Then the Weyl collineations of the Bianchi type V spacetimes are investigated using rank argument of the Weyl matrix. It is obtained that the rank of the 6×6 Weyl matrix for Bianchi type V spacetimes is 0, 4 or 6. It is further shown that these spacetimes do not admit proper Weyl collineations, except in the trivial rank 0 case, which obviously form infinite dimensional Lie algebra. In some special cases it is found that these spacetimes admit Weyl collineations in addition to the Killing vectors, which are in fact proper conformal Killing vectors. The obtained conformal Killing vectors form four-dimensional Lie algebra. |
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| Keywords: | Bianchi type V spacetimes Curvature collineations Weyl collineations Conformal Killing vectors |
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