Classification of Ricci tensor in space-times with a four-parameter group of motions acting on null hypersurfaces

Abstract

The Plebanski type of the Ricci tensor is given for all Bianchi type metrics admitting a four-parameter group of motions acting on null hypersurfaces using the Ludwig-Scanlan classification method and the Newman-Penrose formalism. A class of solutions is found for which the Ricci tensor has a null eigenvector.