THE KARLHEDE CLASSIFICATION OF TYPE-N VACUUM SPACETIMES

The Karlhede classification of a general type N vacuum spacetime is considered and it is found that such spacetimes naturally split into a number of different invariant classes. For each class the canonical forms of the Weyl tensor and its covariant derivatives which are essential for the classification are derived and the upper bound on the order of the covariant derivative of the Weyl tensor required for the classification is analysed, this upper bound being reduced.