On the determination of the energy-momentum tensor and Weyl tensor structure from the curvature in space-time

Consider the curvature tensor components R bcd a on a space-time M calculated from given space-time metric components g ab . The number of alternative space-time metrics for M which yield the same curvature components is known to be heavily restricted, the exact ambiguity in the metric being dependent on the form of the curvature components. In this paper it is shown that, in spite of these ambiguities, the algebraic structure of the energy-momentum tensor and the Weyl tensor on M are essentially determined.