A computer-aided complete classification of geometries in general relativity. First results

Abstract

We report on a computer-aided classification of geometries in terms of the curvature tensor and its covariant derivatives. This extends the Petrov classification to a complete classification of the local geometry and the dimensions of the group of motions and its isotropy subgroup are obtained. As a simple example of the usefulness of the method three of the Harrison metrics are shown to be equivalent.