Space-times admitting a three-parameter similarity group

TL;DR

This paper classifies spacetimes with a three-parameter similarity group, providing their general metric forms based on Bianchi types, which enhances understanding of their geometric structure in general relativity.

Contribution

It offers a comprehensive classification of three-parameter similarity group spacetimes and derives their metric forms based on Bianchi types, filling a gap in geometric analysis.

Findings

Classification based on Bianchi types of the similarity group

Explicit general form of metrics for each case

Enhanced understanding of spacetime symmetries

Abstract

Spacetimes admitting a similarity group are considered. Amongst them, special attention is given to the 3-parameter ones. A classification of such spacetimes is given based on the Bianchi type of the similarity group $H_3$, and the general form of the metric is provided in each case assuming the orbits are non-null.