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Curvature collineations and the determination of the metric from the curvature in general relativity
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For a general class of space-times, it was shown in this paper that the componentsR of the curvature tensor determine the metric components up to a constant conformal factor.Abstract:
It is shown that for a very general class of space-times, the componentsR
of the curvature tensor determine the metric components up to a constant conformal factor This general class contains most of those cases which are usually considered to be interesting from the point of view of Einstein's general relativity theory The connection between the above result and the existence of proper curvature collineations is givenread more
Citations
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Projective Transformations of Pseudo-Riemannian Manifolds
TL;DR: A survey of the results in the theory of projective transformations of pseudo-Riemannian manifolds, in particular, the solution of the classical geometrical problem of determining the Riemannians with corresponding geodesics (Sec. 5) and the Lie problem (Sec 6), can be found in this paper.
Journal ArticleDOI
Spacetimes admitting inheriting conformal Killing vector fields
A. A. Coley,B. O. J. Tupper +1 more
TL;DR: In this article, it was proved that orthogonal synchronous perfect fluid spacetimes, other than Friedmann-Robertson-Walker (FRW), admit no proper inheriting CKV.
Journal ArticleDOI
Algebraic Determination of the Metric from the Curvature in General Relativity
Graham Hall,C. B. G. McIntosh +1 more
TL;DR: In this article, the general solution for a symmetric second-order tensor of the Riemann tensor is given in terms of the curvature 2-form structure of a space-time manifold.
Journal ArticleDOI
Geodesically equivalent metrics in general relativity
TL;DR: In this article, it is shown how to reconstruct a metric from its nonparameterized geodesics, and how to do it effectively if the metric is Ricci-flat.
Journal ArticleDOI
Physical structure of the energy-momentum tensor in general relativity
Graham Hall,D. A. Negm +1 more
TL;DR: The algebraic classification of second-order symmetric tensors based on Segre type is used to give a systematic description of energy-momentum tensors in General Relativity as discussed by the authors.
References
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Journal ArticleDOI
Curvature Collineations: A Fundamental Symmetry Property of the Space‐Times of General Relativity Defined by the Vanishing Lie Derivative of the Riemann Curvature Tensor
TL;DR: In this article, it was shown that the existence of a curvature collineation (CC) is a necessary condition for a covariant generator of field conservation laws in the theory of general relativity.
Journal ArticleDOI
The gravitational compass
TL;DR: In this paper, a purely covariant approach to general relativity, using the equation of geodesic deviation, is adopted, which is essentially that due to Pirani, but instead of using clouds of particles to analyze the gravitational field, a ''gravitational compass'' is proposed which fulfills the same purpose.
Journal ArticleDOI
The classification of the Ricci tensor in general relativity theory
TL;DR: Tangent space null rotations are used to give a straightforward classification of the Ricci tensor in general relativity theory as discussed by the authors, and they are used for the classification of Ricci Tensor.