Exact solutions of Bianchi I spacetimes which admit Conformal Killing vectors

TL;DR

This paper introduces a new classification method for Bianchi I spacetimes based on conformal Killing vectors, applying it to Kasner and other Bianchi I solutions to identify their symmetries.

Contribution

It presents a novel approach linking CKVs of decomposable spaces with their subspaces, enabling classification of Bianchi I spacetimes with conformal symmetries.

Findings

Classified Bianchi I spacetimes admitting CKVs.

Applied method to Kasner spacetime and other solutions.

Identified conditions for maximal symmetry in subspaces.

Abstract

We develop a new method in order to classify the Bianchi I spacetimes which admit conformal Killing vectors (CKV). The method is based on two propositions which relate the CKVs of 1+(n-1) decomposable Riemannian spaces with the CKVs of the (n-1) subspace and show that if 1+(n-1) space is conformally flat then the (n-1) spacetime is maximally symmetric. The method is used to study the conformal algebra of the Kasner spacetime and other less known Bianchi type I matter solutions of General Relativity.