Space-times admitting a three-dimensional conformal group

TL;DR

This paper classifies and explicitly constructs perfect fluid space-times with a three-dimensional conformal symmetry group, focusing on proper conformal motions and their geometric and physical properties.

Contribution

It provides a complete classification of such space-times and derives explicit solutions for various orientations of the fluid velocity relative to the conformal orbits.

Findings

Explicit metrics for classified space-times are presented.

Exact perfect fluid solutions are obtained for different fluid velocity orientations.

The structure of the conformal group influences the form of the solutions.

Abstract

Perfect fluid space-times admitting a three-dimensional Lie group of conformal motions containing a two-dimensional Abelian Lie subgroup of isometries are studied. Demanding that the conformal Killing vector be proper (i.e., not homothetic nor Killing), all such space-times are classified according to the structure of their corresponding three-dimensional conformal Lie group and the nature of their corresponding orbits (that are assumed to be non-null). Each metric is then explicitly displayed in coordinates adapted to the symmetry vectors. Attention is then restricted to the diagonal case, and exact perfect fluid solutions are obtained in both the cases in which the fluid four-velocity is tangential or orthogonal to the conformal orbits, as well as in the more general "tilting" case.