Determination of the metric from the curvature
type: Item
instance of: scholarly article
title: Determination of the metric from the curvature
zbMATH Open document ID: 0760.53021
DOI: 10.1007/BF00759087
author: Hernando Quevedo
published in: General Relativity and Gravitation
publication date: 1993-01-16T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 53B30
Mathematics Subject Classification ID: 83C99
zbMATH DE Number: 95342
zbMATH Keywords: curvature tensor symmetry
zbMATH Keywords: Bianchi identities
reviewed by: G. S. Hall
MaRDI profile type: Publication
cites work: Conditions on a connection to be a metric connection
cites work: Sufficient conditions for a curvature tensor to be Riemannian and for determining its metric
cites work: Q5837114
cites work: A review of the geometrical equivalence of metrics in general relativity
cites work: Determination of the metric tensor from components of the Riemann tensor
cites work: Spacetimes admitting a vector field whose inner product with the Riemann tensor is zero
cites work: Algebraic determination of the metric from the curvature in general relativity
cites work: Curvature collineations and the determination of the metric from the curvature in General Relativity
cites work: The significance of curvature in general relativity
cites work: On the determination of the energy-momentum tensor and Weyl tensor structure from the curvature in space-time
cites work: The uniqueness of \(g_{ij}\) in terms of \(R^l_{ijk}\)
cites work: Curvature structure in general relativity
cites work: Q3263435
cites work: The Gravitational Compass
cites work: A modified equation of geodesic deviation
cites work: Lie derivatives and deviation equations in Riemannian spaces
cites work: Coupled inertial and gravitational effects in the proper reference frame of an accelerated, rotating observer
cites work: Geodesic deviation in the Schwarzschild space-time
cites work: Complex transformations of the curvature tensor
cites work: Q3968096
cites work: Q3896182
cites work: Lorentzian 4 dimensional manifolds with 'local isotropy'
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description: scientific article; zbMATH DE number 95342