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

## TL;DR

This paper establishes new conditions on the Weyl tensor characterizing perfect-fluid generalized Robertson-Walker space-times, and analyzes the Ricci tensor's form via Gray's decomposition, linking geometric properties to physical equations of state.

## Contribution

It provides necessary and sufficient conditions for GRW space-times to be perfect-fluid, and characterizes the Ricci tensor's form using Gray's decomposition, advancing understanding of their geometric and physical structure.

## Key findings

- Weyl tensor conditions for perfect-fluid GRW space-times
- Form of Ricci tensor in Gray's decomposition subspaces
- Connection between Einstein equations and equations of state in 4D

## 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.