Perfect-fluid models admitting a non-Abelian and maximal two-parameter group of isometries

Abstract

A proof is given that, when a spacetime admits an invariant timelike congruence orthogonal to the orbits of a non-Abelian two-parameter group of isometries, the given congruence is vorticity-free provided the group is maximal. The result is used to derive a canonical coordinate form for perfect-fluid solutions satisfying the above condition. It is also shown that such a group of isometries cannot be orthogonally transitive (in agreement with a result by Bugalho (1987)) and a brief discussion is given of the self-similar case.