An Efficient Rif Algorithm for the Classification of Kantowski-Sachs Spacetimes via Conformal Vector Fields

Abstract

In this paper, we classify the Kantowski-Sachs spacetimes via conformal vector fields (CVFs). A Maple algorithm using the ‘Exterior’ package is used to reduce the set of conformal Killing equations to the reduced involutive form (Rif). The algorithm yields a tree, known as the Rif tree, where the branches of the Rif tree give the potential metrics for which the spacetimes under consideration may possess proper CVFs. The set of conformal Killing equations is solved for all the branches of the Rif tree to obtain the explicit forms of CVFs. Some physical implications of the obtained metrics are also discussed.