Perfect-fluid, generalised Robertson-Walker space-times, and Gray's decomposition
General Relativity and Quantum Cosmology
2019-05-31 v2 Mathematical Physics
Differential Geometry
math.MP
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.
Keywords
Cite
@article{arxiv.1901.04070,
title = {Perfect-fluid, generalised Robertson-Walker space-times, and Gray's decomposition},
author = {Carlo Alberto Mantica and Luca Guido Molinari and Young Jin Suh and Sameh Shenawy},
journal= {arXiv preprint arXiv:1901.04070},
year = {2019}
}
Comments
10 pages, final version