Conformally Einstein Perfect Fluid Spacetimes

Norbert Van den Bergh

The Geroch-Held-Penrose formalism is used to give a streamlined overview of the results obtained in the past decades for conformally Ricci-flat and conformally Einstein perfect fluid spacetimes. These are spacetimes for which the Ricci-tensor is of Segre type [(111)1] and for which the metric is conformally related to the metric of an Einstein space. If, in particular, the latter is vacuum the spacetime is called conformally Ricci-flat. After discussing the by now classical results for the case of shear-free or vorticity-free perfect fluids, I present some new results and I point out a few avenues for further research in this area.