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Title of Thesis

Projective and Curvature Symmetries in non-static Space Times Intelligent View Extrapolation for Dynamic Scenes

Author (s)
Muhammad Ramzan
Institute/University/Department Details
Ghulam Ishaq Khan Institute of Engineering Sciences and Technology
Session
2009
Subject
Mathematics
Number of Pages
130
Keywords (Extracted from title, table of contents and abstract of thesis)
non static specetimes, infinite dimensional vector space, collineations 

Abstract

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 nonstatic 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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1590 KB

S. No. Chapter Title of the Chapters Page Size (KB)
  0    
       
1 1 Preliminaries 1
       
2 2 Symmetries in General Relativity 9
125 KB
       
       
 
3 3 Proper Curvature Collineations in Non-Static Spherically Symmetric and Non-Static Plane Symmetric Spacetimes 23
  3.1 Introduction 23

142 KB

 

  3.2 Proper Curvature Collineations in Non-Static Spherically Symmetric Spacetimes 23
  3.3 Proper Curvature Collineations in Non-Static Plane Symmetric Spacetimes 32
  3.4 Conclusions 39
       
       
       
4 4 Proper Curvature Collineations in Non-Static Cylindrically Symmetric and Special Non-Static Axially Symmetric Spacetimes 50
  4.1 Introduction 50
  4.2 Proper Curvature Collineations in Non-Static Cylindrically Symmetric Spacetimes 50


245 KB

  4.3 Proper Curvature Collineations in Special Non-Static Axially Symmetric Spacetimes 79
  4.4 Conclusions 94
       
       
5 5 Proper Projective Symmetry in Special Non-Static Plane Symmetric Spacetimes 96
125 KB
  5.1 Introduction 96
  5.2 Projective Symmetry 96
  5.3 Main Results 97
  5.4 Conclusion 117
       
       
       

14 KB

       
       
6 6 References 118