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Concircular curvature tensor and fluid spacetimes. (English) Zbl 1255.83110

Summary: In the differential geometry of certain \(F\)-structures, the importance of concircular curvature tensor is very well known. The relativistic significance of this tensor has been explored here. The spacetimes satisfying Einstein field equations and with vanishing concircular curvature tensor are considered and the existence of Killing and conformal Killing vectors have been established for such spacetimes. Perfect fluid spacetimes with vanishing concircular curvature tensor have also been considered. The divergence of concircular curvature tensor is studied in detail and it is seen, among other results, that if the divergence of the concircular tensor is zero and the Ricci tensor is of Codazzi type then the resulting spacetime is of constant curvature. For a perfect fluid spacetime to possess divergence-free concircular curvature tensor, a necessary and sufficient condition has been obtained in terms of Friedmann-Robertson-Walker model.

MSC:

83E05 Geometrodynamics and the holographic principle
83C15 Exact solutions to problems in general relativity and gravitational theory
53Z05 Applications of differential geometry to physics
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