I= CURVATURE COLLINEATIONS OF SOME SPACETIMES AND THEIR PHYSICAL INTERPRETATION
Pakistan Research Repository Home
 

Title of Thesis
CURVATURE COLLINEATIONS OF SOME SPACETIMES AND THEIR PHYSICAL INTERPRETATION

Author(s)
Abdul Rehman Kashif
Institute/University/Department Details
Department of Mathematics/ Quaid-i-Azam 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.

Download Full Thesis
2476.18 KB
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