Perfect fluid space-times admitting a 3-dimensional conformal group acting on null orbits

TL;DR

This paper classifies perfect fluid space-times with a 3D conformal symmetry acting on null orbits, providing explicit metrics and CKVs, but finds none satisfy all energy conditions globally.

Contribution

It offers a comprehensive classification of such space-times and explicit metric forms, expanding understanding of conformal symmetries in perfect fluid models.

Findings

Explicit metrics and CKVs for these space-times

No solutions satisfy weak and dominant energy conditions everywhere

Complete classification of perfect fluid solutions with this symmetry

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 then provided (irrespectively of the matter content) and all possible perfect fluid solutions are found, although none of them verifies the weak and dominant energy conditions over the whole space-time manifold.