Killing vector fields of Bianchi type I spacetimes via Rif tree approach

Abstract

In this paper, we have adopted a new approach to study the Killing vector fields of locally rotationally symmetric and general Bianchi type I spacetimes. Instead of directly integrating the set of Killing’s equations, an algorithm is developed in Maple which converts these equations to the reduced involutive form (Rif) and consequently it imposes some restrictions on the metric functions in the form of a tree, known as Rif tree. The set of Killing’s equations is then solved for each branch of the Rif tree, giving the explicit form of the Killing vector fields. The structure of Lie algebra is presented for each set of the obtained Killing vector fields and some physical implications of the obtained metrics are discussed.