Algebraic determination of the metric from the curvature in general relativity

DOI10.1007/BF02083290zbMath0523.53037OpenAlexW2082743316MaRDI QIDQ1056393

Colin B. G. McIntosh, Graham S. Hall

Publication date: 1983

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02083290

Mathematics Subject Classification ID

Applications of local differential geometry to the sciences (53B50) Local Riemannian geometry (53B20) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items

Sufficient conditions for a curvature tensor to be Riemannian and for determining its metric, Curvature collineations in general relativity. I, Curvature collineations in general relativity. II, Connections and symmetries in spacetime, Curvature and conformal collineations in presence of matter, Weyl compatible tensors, The curvature problem in general relativity, Uniqueness of the metric from the Weyl and energy-momentum tensors, PROPER PROJECTIVE SYMMETRY IN KANTOWSKI–SACHS AND BIANCHI TYPE III SPACETIMES, A complete classification of curvature collineations of cylindrically symmetric static metrics, Purely magnetic space–times, Holonomy groups in general relativity, Curvature structure in general relativity, A note on proper projective collineation in special Bianchi type I space-times, Perfect fluid spacetimes admitting curvature collineations, PROPER PROJECTIVE SYMMETRY IN SPHERICALLY SYMMETRIC STATIC SPACE–TIMES, Determination of the metric from the curvature, Projective symmetry in null Einstein–Maxwell space-times, Constructing a space from the geodesic equations, Killing-Yano tensors in general relativity, Symmetries and geometry in general relativity, Parallel metrics and reducibility of the holonomy group, Insufficiency of the Ricci and Bianchi identities for characterising curvature, PROPER PROJECTIVE SYMMETRY IN THE SCHWARZSCHILD METRIC, Some remarks on the converse of Weyl's conformal theorem, The significance of curvature in general relativity

Cites Work

• Mappings of empty space-times leaving the curvature tensor invariant
• The uniqueness of \(g_{ij}\) in terms of \(R^l_{ijk}\)
• Conservation laws in general relativity based upon the existence of preferred collineations
• The holonomy group in general relativity and the determination of \(g_{iJ}\) from \(T^{i_j}\)
• Determination of the metric tensor from components of the Riemann tensor
• The Regularization of Nonlinear Electrical Circuits
• The classification of the Ricci tensor in general relativity theory
• On the Geometry of the Riemann Tensor
• The Gravitational Compass
• Curvature Collineations: A Fundamental Symmetry Property of the Space-Times of General Relativity Defined by the Vanishing Lie Derivative of the Riemann Curvature Tensor