Curvature properties of Robinson–Trautman metric
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In this paper, the curvature properties of the Robinson-Trautman metric have been investigated and it is shown that the Ricci tensor is Riemann compatible and its Weyl conformal curvature 2-forms are recurrent.Abstract:
The curvature properties of Robinson–Trautman metric have been investigated. It is shown that Robinson–Trautman metric is a Roter type metric, and in a consequence, admits several kinds of pseudosymmetric type structures such as Weyl pseudosymmetric, Ricci pseudosymmetric, pseudosymmetric Weyl conformal curvature tensor etc. Moreover, it is proved that this metric is a 2-quasi-Einstein, the Ricci tensor is Riemann compatible and its Weyl conformal curvature 2-forms are recurrent. It is also shown that the energy momentum tensor of the metric is pseudosymmetric and the conditions under which such tensor is of Codazzi type and cyclic parallel have been investigated. Finally, we have made a comparison between the curvature properties of Robinson–Trautman metric and Som–Raychaudhuri metric.read more
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On Curvature properties of Nariai Spacetimes
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References
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Exact Solutions of Einstein's Field Equations
TL;DR: A survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources can be found in this paper, where the solutions are ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties.
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An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation
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Tensors, differential forms, and variational principles
David Lovelock,Hanno Rund +1 more
TL;DR: A self-contained, reasonably modern account of tensor analysis and the calculus of exterior differential forms, adapted to the needs of physicists, engineers and applied mathematicians is presented.