الفهرس 
Riemannian Geometry
The Raychaudhuri EquationOnly 14 pages are availabe for public view
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Abstract
This thesis is devoted to analyzing and giving a suggested solution to one of the problems of general relativity (GR). The problem is the initial singularity problem which appears in the applications of GR in the domain of cosmology. We give a brief review on GR and its applications in the domain of cosmology, then we give an account on the standard treatment of the initial singularity and the singularity theorems. Some authors have argued that the main problem of GR is that its field equations contain apart which is not geometric. They formulated a type of field theories depending on pure geometric considerations. This type is termed pure geometric field theories. We examined the existence of the initial singularity in this type. The geometry used for this study is the parameterized absolute parallelism geometry. We show that the parameter of this geometry, causing a type of interaction called spin- torsion interaction strongly affects the existence of initial singularity. The geometric conditions for the existence of this singularity are given. We show also that the existence of this singularity is dependent neither on the sectional curvature of space-time nor on the signature of the metric. The main results of this thesis are published in a joint paper by the author, reference [74] in the list of references at the end of this thesis.