Symmetries of Bianchi I space-times

TL;DR

This paper classifies diagonal Bianchi I space-times based on their symmetries, explicitly deriving the metrics and symmetry vectors, and discusses physical implications including a new anisotropic fluid solution with conformal symmetry.

Contribution

It provides a comprehensive classification of Bianchi I space-times admitting various symmetries, with explicit metric forms and symmetry vectors, and introduces a new physically valid anisotropic fluid solution.

Findings

Explicit forms of metrics for various symmetries

Symmetry vectors are explicitly computed

New anisotropic fluid solution with conformal symmetry

Abstract

All diagonal proper Bianchi I space-times are determined which admit certain important symmetries. It is shown that for Homotheties, Conformal motions and Kinematic Self-Similarities the resulting space-times are defined explicitly in terms of a set of parameters whereas Affine Collineations, Ricci Collineations and Curvature Collineations, if they are admitted, they determine the metric modulo certain algebraic conditions. In all cases the symmetry vectors are explicitly computed. The physical and the geometrical consequences of the results are discussed and a new anisitropic fluid, physically valid solution which admits a proper conformal Killing vector, is given.