Determination of the metric from the curvature
This paper considers further the problem of determining the metric of space-time from the curvature tensor. However, the reviewer finds it difficult to see exactly, what the author has achieved, because of the confusion, that sets in during the early stages of the paper. The author's review of what has been achieved so far in the literature is misleading. Also the discussion of the physical determination of the curvature components using the well known results of Pirani and Szekeres overlooks the fact that a knowledge of the metric is required in these determinations. In the setting up of the mathematical part of the paper the author is somewhat vague as to what constitutes the Petrov types since such a classification requires a metric (or at least a bivector metric). Also he uses the ``result'' that a tensor \(T_{abcd}\) with curvature tensor symmetry and satisfying the Bianchi identities with respect to some connection is necessarily a curvature tensor associated with some metric. This is false as \textit{A. D. Rendall} [J. Geom. Phys. 6, No. 1, 159-163 (1989; Zbl 0681.53007)] has recently shown. There seems to be a general confusion throughout the paper between the specification of the coordinate components of the Riemann tensor and its tetrad components. The author seems to pass between them freely whereas, so far as the reviewer knows, no clear link between them has been established.
scientific article; zbMATH DE number 95342
scientific article