Proper homothetic vector fields of Bianchi type I spacetimes via Rif tree approach

Abstract

This paper deals with the study of homothetic vector fields of Bianchi type I spacetimes using Rif tree approach. Instead of directly integrating the homothetic symmetry equations, a computer algorithm is used to transform these equations to the reduced involutive form, which splits the problem of integrating these equations into many cases and gives these cases in the form of a tree imposing certain restrictions on the metric functions. Using these restrictions, the set of homothetic symmetry equations is solved to get the explicit form of the metrics and their homothetic vector fields. It is observed that this approach gives some new physically realistic metrics, not given by an earlier study through direct integration technique.

Keywords

• Homothetic vector fields
• Bianchi type I spacetimes
• Reduced involutive form