Classification of Kantowski–Sachs metric via conformal Ricci collineations

Abstract

In this paper, we present a classification of the Kantowski–Sachs spacetime metric according to its conformal Ricci collineations (CRCs). Solving the CRC equations, it is shown that the Kantowski–Sachs metric admits 15-dimensional Lie algebra of CRCs when its Ricci tensor is non-degenerate and an infinite dimensional group of CRCs when the Ricci tensor is degenerate. Some examples of Kantowski–Sachs metric admitting nontrivial CRCs are presented and their physical interpretation is provided.