Spaces conformal to a class of spaces in general relativity

Source abstract

Abstract A study of conform al transformations of a Riemannian V4 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.