KHALID, SAIFULLAH
(2002)
*RICCI COLLINEATIONS OF CYLINDRICALLY SYMMETRIC STATIC SPACETIME.*
Doctoral thesis, Quaid-i-Azam University Islamabad, Pakistan.

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## Abstract

Symmetries are used in general relativity not only to find the exact solutions of the Einstein Field Equations (EFE), but some of them provide invariant bases for the classification of spacetimes as well. Killing vectors (KVs), homothetic motions (HMs) and Ricci collineations (RCs) are some of these symmetries. In this thesis RCs are used to serve both of these purposes. A complete classification of cylindrically symmetric static spacetimes according to their RCs is provided. After the introductory chapter, where a survey of the related literature is given, we have obtained the RCs for the non-degenerate as well as the degenerate Ricci tensor. We have also provided their Lie algebras. It is found that the Lie algebras of the RCs of these spacetimes, for the non-degenerate Ricci tensor have dimension ranging from 3 to 10 excluding 8 and 9. For t.he degenerate case the Lie algebras are mostly infinite dimensional. However, cases of the algebras of dimensions 3, 4, 5 and10 have also been found. The comparison of the RCs with the KVs and HMs has given rise to numerous interesting cases of proper (or non-isometric) RCs. Corresponding to each Lie algebra there arise differential constraints (mostly non-linear) on the metric coefficients. We have solved these constraints to construct examples of metrics which include some exact solutions admitting proper RCs. Their physical interpretation is also given. The classification of plane symmetric static spacetimes emerges as a special case of this classification when the cylinder is unfolded. Some results are summarized in the form of theorems in the concluding chapter.

Item Type: | Thesis (Doctoral) |
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Uncontrolled Keywords: | cylindrically symmetric static spacetime, ricci collineations, einstein field equations, killing vectors, homothetic motions, lie derivative, ricci tensor |

Subjects: | Q Science > QA Mathematics |

Depositing User: | Muhammad Khan Khan |

Date Deposited: | 26 Sep 2016 09:54 |

Last Modified: | 26 Sep 2016 09:54 |

URI: | http://eprints.hec.gov.pk/id/eprint/1603 |

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