Perfect-fluid, generalized Robertson-Walker space-times, and Gray’s decomposition

We give new necessary and sufficient conditions on the Weyl tensor for generalized Robertson-Walker (GRW) space-times to be perfect-fluid space-times. For GRW space-times, we determine the form of the Ricci tensor in all the O(n)-invariant subspaces provided by Gray’s decomposition of the gradient o...

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Bibliographic Details
Published in:Journal of mathematical physics 2019-05, Vol.60 (5), p.52506
Main Authors: Mantica, Carlo Alberto, Molinari, Luca Guido, Suh, Young Jin, Shenawy, Sameh
Format: Article
Language:English
Subjects:
Decomposition
Einstein equations
Equations of state
Mathematical analysis
Physics
Spacetime
Subspaces
Tensors
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Summary:We give new necessary and sufficient conditions on the Weyl tensor for generalized Robertson-Walker (GRW) space-times to be perfect-fluid space-times. For GRW space-times, we determine the form of the Ricci tensor in all the O(n)-invariant subspaces provided by Gray’s decomposition of the gradient of the Ricci tensor. In all but one, the Ricci tensor is Einstein or has the form of perfect fluid. We discuss the corresponding equations of state that result from the Einstein equation in dimension 4, where perfect-fluid GRW space-times are Robertson-Walker.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.5089040