Classification of spacetimes according to conformal Killing vectors

TL;DR

This paper classifies spacetimes based on conformal Killing vectors, revealing how special vectors like homothetic and Killing vectors are subsets of CKVs, thus providing a systematic understanding of spacetime symmetries.

Contribution

It introduces a classification scheme for spacetimes using conformal Killing vectors, highlighting the relationships among CKVs, homothetic vectors, and Killing vectors.

Findings

Homothetic and Killing vectors are subsets of CKVs.

Classification results show how different vectors relate within spacetime symmetries.

Provides a framework for understanding spacetime symmetries through CKVs.

Abstract

Conformal Killing vectors (CKVs) preserve the spacetime metric up to a factor. Homothetic vectors and Killing vectors are special cases of CKVs. Classification of some classes of spacetimes on the basis of CKVs give interesting results showing how homothetic and Killing vectors which form subsets of the set of CKVs can be recovered as a result of the above classification.