Group Theoretic Techniques for Solutions of Einstein Equations

Abstract

General relativity is a physical theory which plays a key role in astrophysics and is impor- tant for a number of ambitious experiments and space missions. Einstein field equations are basic equations of general relativity and are expressed in terms of coupled highly non- linear partial differential equations describing the matter content of space-time. For this reason it is clear that the theory of partial differential equations is of immense importance in the study of Einstein field equations. The investigations carried out are confined to the applications of the group-theoretic methods, symmetry reduction method, Painlev´e analysis and Generalized G′ G - expansion method to the system of nonlinear partial differ- ential equations arising in general relativity and other important physical phenomenon from mathematical physics. The thesis entitled GROUP THEORETIC TECHNIQUES FOR SOLUTIONS OF EINSTEIN EQUATIONS comprises eight chapters. This thesis is a condensed re- view of the exact solutions of Einstein field equations and ensuing phenomena.