Perfect-fluid, generalised Robertson-Walker space-times, and Gray's decomposition

Abstract

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.

arXiv comment10 pages, final version

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• Gradient conformal stationarity and the CMC condition in LRS spacetimes
• Sufficient conditions for a pseudosymmetric spacetime to be a perfect fluid spacetime
• Curvature conditions for spatial isotropy