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

Authors:
  • CMCarlo Alberto Mantica
    Carlo Alberto Mantica
  • LMLuca Guido Molinari
    Luca Guido Molinari
  • YSYoung Jin Suh
    Young Jin Suh
  • SSSameh Shenawy
    Sameh Shenawy
Preprint
Publisher website
Google Scholar
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.