Spaces conformal to a class of spaces in general relativity

Abstract
A study of conform al transformations of a Riemannian V 4 is made within the framework of the Penrose spinor formalism . In particular the conformal properties of a whole hierarchy of spaces occurring in general relativity are considered, and necessary and sufficient conditions are established for a space to be conform al ( a ) to a space in which the conform tensor is divergence-free, ( b ) to an empty space, ( c ) to an Einstein space. The case of Petrov type N has to be treated separately.