Cosmic String in theory of General Relativity

Abstract

This thesis is organized as follows. Chapter I contains a brief discussion of the production of various topological defects in cosmological phase transitions in the early universe. The three kinds of topological defects associated with spontaneous symmetry breaking: domain wall, cosmic string and magnetic monopole. The existence and stability of these defects is dictated by topological considerations. This chapter also includes a discussion on the standard cosmology and cosmological phase transitions. In the chapter II we review some physical properties of the cosmic string. Pair of cosmic sttings intercommuting at two points can form closed loops. A closed loop will oscillate, gradually loosing energy , until it disappear. Only significant energy loss mechanism is gravitational radiation. Gravitational radiation is indeed dominant. There is no local gravitational field due to the cosmic string. The cosmic string acts as a gravitational lens for both light rays and particles. Chapter ill addresses the topic of cosmic string evolution and structure formation. In the chapter IV we give a brief account of the Plebanski space-time. The Plebanski space-time includes many interesting space-times which are not black hole space-times but are important from the physical point of view. In the chapter V we study the equilibrium configurations of a cosmic string described by the Nambu-action in the NUT-Kerr-Newman space-time which includes as special cases the Kerr-Newman black hole space-time as well as NUT space-time which is considered as cosmological model. In this study it is interesting to note that one can obtain parallel results for Kerr-Newman black hole as well as for NUT space-time. Finally, in the chapter VI we study the equilibrium configurations of a cosmic string described by the Nambu-action in curved space-time such as the Kerr­Newman-Kasuya space-time which is the Kerr-Newman space-time involved with extra magnetic monopole charge. In this study it is interesting to note that the physical results remain the same whether or not the magnetic monopole exist in nature.