Classification of Axially Symmetric Space-time According to Ricci Tensor Symmetries

Abstract

In this paper, we study the classification of axially symmetric space-time according to Ricci symmetries (collineations). These classifications have been studied for the cases when one component of Ricci symmetry vector field V is non-zero for the cases 1 to 4, two components of V are non-zero in cases 5 to 10 and three components of V are non-zero in cases 11 to 14 respectively. It is observed that, when Ricci tensor  is non-degenerate, the Ricci symmetry is finite dimensional, and, when Ricci tensor R_ab is degenerate, we cannot confirm finite dimensionality of Ricci symmetry. Finally, we discuss the results in detail.