On the geometry of null congruences in general relativity

Some theorems for the null conguences within the framework of general theory of relativity are given. These theorems are important in themselves as they illustrate the geometric meaning of the spin coefficients. The newly developed Geroch-Held-Penrose (GHP) formalism has been used throughout the investigations. The salient features of GHP formalism that are necessary for the present work are given, and these techniques are applied to a pair of null congruences C (l) and C(n).