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Projective and Curvature Symmetries in Non-Static Spacetimes

Thesis Info

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Author

Ramzan, Muhammad

Program

PhD

Institute

Ghulam Ishaq Khan Institute of Engineering Sciences and Technology

City

Topi

Province

KPK

Country

Pakistan

Thesis Completing Year

2009

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/102

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727036172

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The aim of this thesis is to study the projective and curvature symmetries in non-static spacetimes. A study of non-static spherically symmetric, non-static plane symmetric, non-static cylindrically symmetric and special non-static axially symmetric spacetimes according to their proper curvature collineations (CCS) is given by using the rank of the 6 × 6 Riemann matrix and direct integration techniques. We consider the non-static spherically symmetric spacetimes to investigate proper CCS. It has been shown that when the above spacetimes admit proper CCS, they turn out to be static spherically symmetric and form an infinite dimensional vector space. In the non- static cases CCS are just Killing vector fields. In case of non-static plane symmetric spacetimes, it has been shown that when above spacetimes admit proper CCS, they form an infinite dimensional vector space. We consider the non-static cylindrically symmetric and special non-static axially symmetric spacetimes to study the proper CCS. It has been investigated that when above spacetimes admit proper CCS, they also form an infinite dimensional vector space. We consider the special non-static plane symmetric spacetimes to investigate proper projective collineations. Following an approach developed by G. Shabbir in [39], which basically consists of some algebraic and direct integration techniques to study proper projective collineations in the above spacetimes. It has been shown that when the above spacetimes admit proper projective collineations, they become a very special class of the spacelike or timelike versions of FRW K=0 model.
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شاہ ودود احمد

شاہ ودود احمد
قارئین کو یہ خبر سن کر بھی بڑا ملال ہوگا کہ رمضان المبارک کے دوسرے عشرہ میں مولانا شاہ معین الدین احمد ندوی مرحوم سابق اڈیٹر معارف کے صاحبزادے شاہ ودود احمد کا انتقال حرکت قلب بند ہوجانے سے کراچی میں ہوگیا۔ اپنے والد بزرگوار ہی کی طرح وہ بھی بڑے نیک طینت اور شریف النفس انسان تھے، ان کی تعلیم شبلی کالج میں ہوئی اور تقسیم کے بعد پہلے ڈھاکہ پھر کراچی گئے جہاں پیام اجل آگیا۔ اﷲ تعالیٰ غریق رحمت کرے اور تمام پس ماندگان خصوصاً ان کی بیوہ، بیٹے اور بیٹی کو صبرِجمیل عطا فرمائے، آمین۔ (ضیاء الدین اصلاحی، اپریل ۱۹۹۴ء)

 

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