Petrov D vacuum spaces revisited: Complete tables and invariant classification by GHP analysis

Abstract

The efficiency of the GHP formalism combined with the power of the computer system xAcT enables an exhaustive systematic analysis to be made of Petrov D vacuum spaces. This gives a complete involutive set of tables for the four GHP derivatives on each of the four GHP spin coefficients and the one Weyl tensor component. It follows directly from these results that the theoretical upper bound on the order of covariant differentiation of the Riemann tensor required for a Karlhede invariant classification of these spaces is reduced to two.