Lie groups of conformal motions acting on null orbits

TL;DR

This paper classifies space-times with a 3D Lie group of conformal motions acting on null orbits, providing metric forms and CKVs, and finds all perfect fluid solutions that do not satisfy energy conditions globally.

Contribution

It offers a comprehensive analysis of conformal symmetries in null orbit space-times and derives all compatible perfect fluid solutions, expanding understanding of such geometries.

Findings

Derived coordinate expressions for metrics and CKVs.

Found all perfect fluid solutions with these symmetries.

None of the solutions satisfy energy conditions everywhere.

Abstract

Space-times admitting a 3-dimensional Lie group of conformal motions $C_3$ acting on null orbits are studied. Coordinate expressions for the metric and the conformal Killing vectors (CKV) are provided (irrespectively of the matter content) and then all possible perfect fluid solutions are found, although none of these verify the weak and dominant energy conditions over the whole space-time manifold.