Null Tetrad Approach to Motions in Empty Space-Time

Abstract

The integrability conditions of conformal motions are written in the null tetrad formalism of Newman and Penrose. The maximum order of the group of conformal motions admitted by nonflat empty space-times of given Petrov type is shown to be at most one greater than the maximum order of the group of Killing motions. The symmetries of those empty space-times which possess hypersurface orthogonal geodesic rays with nonvanishing divergence are determined. Among these space-times is one of type III which admits a group of Killing motions of order three. This provides a counter example to a result of Petrov which states that the maximum order of the group of Killing motions for such space-times is two.