Computer-aided classification of the Ricci tensor in general relativity

Methods of classification of the Ricci tensor (and hence the energy-momentum) in general relativity are reviewed, and their geometric interpretation considered. It is shown that the Plebanski spinor represents the map of self-dual bivectors naturally induced from the map of vectors defined by the Ricci tensor. It is noted that in some cases the multiplicities for the Petrov classification of the Plebanski spinor and the eigenvalue equation of the Ricci spinor differ; as direct computation of roots is more difficult than finding their multiplicities, an algorithm is devised which exploits this difference. Details of the algorithm, including methods for distinguishing the sub-cases not separated by the multiplicities mentioned, are given, and the resulting computer program described. Test results are reported.