Curvature collineations and the determination of the metric from the curvature in General Relativity

DOI10.1007/BF00759572zbMath0514.53018OpenAlexW2018253025MaRDI QIDQ1051272

Graham S. Hall

Publication date: 1983

Published in: General Relativity and Gravitation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00759572

zbMATH Keywords

spacetimegeodesic deviationcurvature collineationscomponents of the Riemann tensordetermination of the metric

Mathematics Subject Classification ID

Gravitational energy and conservation laws; groups of motions (83C40) Applications of local differential geometry to the sciences (53B50) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

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Cites Work

• Mappings of empty space-times leaving the curvature tensor invariant
• The uniqueness of \(g_{ij}\) in terms of \(R^l_{ijk}\)
• Symmetry mappings in Einstein-Maxwell space-times
• The Riemann tensor, the metric tensor, and curvature collineations in general relativity
• The classification of the Ricci tensor in general relativity theory
• 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