

Title of Thesis
CURVATURE COLLINEATIONS OF SOME SPACETIMES AND THEIR PHYSICAL INTERPRETATION 
Author(s)
Abdul Rehman Kashif 
Institute/University/Department Details
Department of Mathematics/ QuaidiAzam University 
Session
2003 
Subject
Mathematics 
Number of Pages
199 
Keywords (Extracted from title, table of contents and abstract of thesis)
curvature collineations, some spacetimes, riemann tensor, metric tensor, ricci collineations, ricci tensor, spherically symmetric, plane symmetric, cylindrically symmetric, static spacetimes, homothetic vectors, killing vectors 
Abstract Curvature collineations are symmetry directions for the Riemann tensor, in the same sense as isometries are for the metric tensor and Ricci collineations for the Ricci tensor. Complete listings of many metrics possessing some minimal symmetry have been given for a number of symmetry groups for their curvature collineations. Special emphasis is placed on the study of spherically symmetric (Chapter 2), plane symmetric (Chapter 3), cylindrically symmetric (Chapter 4) static spacetimes, and their comparison with Ricci collineations, homothetic vectors and Killing vectors. The Einstein field equations are then used as defining equations for the stress energy tensor. The metrics obtained are investigated for their physical interpretation. It turns out that in this complete list, there are curvature collineations that are distinct from the set of isometries, homothetic vectors and of Ricci collineations. The work in Chapter 2 appeared in: J. Math. Phys. 38 (1997)3639; (prior to this thesis) and Nuovo Cimento 8115 (2000)281; Chapter 3 in: J. Math. Phys. 44 (2000)2167; and Chapter 4 has been accepted in: Gen. Ref. Grav. 35 (2003). My journal article contributions are attached to the last part of the thesis. In this process, all of the known spherically symmetric, plane symmetric and cylindrically symmetric static metrics are recovered along with their symmetry groups. Some metrics and classes of metrics, according to their curvature collineations, (different from RCs, HVs and KVs) are found which were not obtained before. Finally, in the concluding Chapter 5, a summary of the results obtained, main findings as theorems and some open problems are mentioned.






S. No. 
Chapter 
Title of the Chapters 
Page 
Size (KB) 





1 
0 
Contents 

87.59 KB 





2 
1 
Preliminaries 
1 
247.83 KB 

1.1 
Introduction 
1 

1.2 
Basics 
8 





3 
2 
Curvature Collineations of Spherically Symmetric Static Spacetimes 
23 
466.54 KB 

2.1 
Introduction 
23 

2.2 
The Classification 
23 

2.3 
Classification of CCs Case (I ) 
28 

2.4 
Classification of CCs Case ( ll ) 
40 

2.5 
Comparison of CCs with KVs , HV sand RCs 
43 

2.6 
Petrov Classification of Spherically Symmetric Static Spacetimes 
52 

2.7 
Segre Classification of Spherically Symmetric Static Spacetimes 
53 

2.8 
Algebra for Spherically Symmetric Static Spacetimes 
54 

2.9 
Conclusion 
58 





4 
3 
Curvature Collineations of Plane Symmetric Static Spacetimes 
61 
467.09 KB 

3.1 
Introduction 
61 

3.2 
The Classification 
61 

3.3 
Comparison of CCs with KV s, HV sand RCs 
79 

3.4 
Petrov Classification of Plane Symmetric Static Spacetimes 
87 

3.5 
Segre Classification of Plane Symmetric Static Spacetimes 
90 

3.6 
Algebra for Plane Symmetric Static Spacetimes 
91 

3.7 
Conclusion 
93 





5 
4 
Curvature Collineations of Cylindrically Symmetric Static Spacetimes 
97 
659.42 KB 

4.1 
Introduction 
97 

4.2 
The Classification 
97 

4.3 
Comparison of CCs with KV s, HV sand RCs 
116 

4.4 
Petrov Classification of Cylindrically Symmetric Static Spacetimes 
131 

4.5 
Segre Classification of Cylindrically Symmetric Static Spacetimes 
133 

4.6 
Algebra for Cylindrically Symmetric Static Spacetimes 
134 

4.7 
Conclusion 
137 





6 
5 
Conclusion 
141 
772.5 KB 

5.1 
References 
150 

5.2 
Published work 






