Non-vacuum twisting type N metrics

Abstract

A maximally reduced system of equations corresponding to the twisting type N Einstein metrics is given. When the cosmological constant $λ\to 0$ they reduce to the standard equations for the vacuum twisting type N's. All the metrics which are conformally equivalent to the twisting type N metrics and which admit 3-dimensional conformal group of symmetries are presented. In the Feferman class of metrics an example is given of a twisting type N metric which satisfies Bach's equations but is not Einstein.