Mappings of empty space-times leaving the curvature tensor invariant

DOI10.1007/BF00756191zbMath0486.53046MaRDI QIDQ1164870

C. D. Collinson, Estelita Da Grace Lopes Rodrigues Vaz

Publication date: 1982

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

zbMATH Keywords

Ricci tensorPetrov typeempty space-time metric

Mathematics Subject Classification ID

Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory (83C20) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50)

Related Items (10)

Sufficient conditions for a curvature tensor to be Riemannian and for determining its metric ⋮ The curvature problem in general relativity ⋮ Conformally Ricci-flat perfect fluids. II ⋮ Incorporation of space–time symmetries in Einstein’s field equations ⋮ Symmetries and geometry in general relativity ⋮ Irreducible decomposition of Einstein's equations in spacetimes with symmetries ⋮ Curvature collineations and the determination of the metric from the curvature in General Relativity ⋮ Curvature collineations for type-N Robinson-Trautman space-times ⋮ Algebraic determination of the metric from the curvature in general relativity ⋮ The significance of curvature in general relativity

Cites Work

• The uniqueness of \(g_{ij}\) in terms of \(R^l_{ijk}\)
• The holonomy group in general relativity and the determination of \(g_{iJ}\) from \(T^{i_j}\)
• Some spherical gravitational waves in general relativity
• Determination of the metric tensor from components of the Riemann tensor
• The Gravitational Compass
• Symmetries of type N empty space-times possessing twisting geodesic rays

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