'Degenerate' nondegenerate spacetime metrics

Abstract

In the Petrov classification (1969) of the Weyl tensor (or spinor), the type I or (1111) case is referred to in the literature as non-degenerate; there is, however, a 'degenerate' class of type I metrics in which the four distinct principal null directions (PND) only span a 3-space at each point; the degeneracy refers to the dimension of the space of PND. This subcase is shown to exist when I3/J2)6. Metrics of the Kasner type provide an important example of the two type I cases, and an illustration of the kind of geometrical insight into the structure of spacetime metrics which is afforded by analysis of the space of PND.