Curvature Tensor for the Spacetime of General Relativity

In the differential geometry of certain F-structures, the role of W-curvature tensor is very well known. A detailed study of this tensor has been made on the spacetime of general relativity. The spacetimes satisfying Einstein field equations with vanishing W-tensor have been considered and the exist...

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Bibliographic Details
Published in:arXiv.org 2016-02
Main Authors: Ahsan, Zafar, Musavvir Ali
Format: Article
Language:English
Subjects:
Astronomical models
Cosmology
Curvature
Differential geometry
Divergence
Einstein equations
Fields (mathematics)
Mathematical analysis
Relativity
Spacetime
Tensors
Theory of relativity
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Summary:In the differential geometry of certain F-structures, the role of W-curvature tensor is very well known. A detailed study of this tensor has been made on the spacetime of general relativity. The spacetimes satisfying Einstein field equations with vanishing W-tensor have been considered and the existence of Killing and conformal Killing vector fields has been established. Perfect fluid spacetimes with vanishing W-tensor have also been considered. The divergence of W-tensor is studied in detail and it is seen, among other results, that a perfect fluid spacetime with conserved W-tensor represents either an Einstein space or a Friedmann-Robertson-Walker cosmological model.
ISSN:2331-8422