An algorithmic classification of geometries in general relativity

Abstract

The complicated coordinate transformations in general relativity make coordinate invariant classification schemes extremely important. A computer program, written in SHEEP, performing an algorithmic classification of the curvature tensor and a number of its derivatives is presented. The output is a complete description of the geometry. The problem to decide whether or not two solutions of Einstein's equations describe the same gravitational field can be solved if the (non-) existence of a solution to a set of algebraic equations can be established. The classification procedure has been carried through for a number of fields, and solutions previously believed to describe physically different situations have been shown to be equivalent. We exemplify with a physically interesting class of geometries.