A condition for a perfect-fluid space-time to be a generalized Robertson-Walker space-time

TL;DR

This paper establishes conditions under which a perfect-fluid space-time with specific properties is equivalent to a generalized Robertson-Walker space-time with an Einstein fiber, linking geometric and physical criteria.

Contribution

It provides a new characterization of generalized Robertson-Walker space-times based on the divergence of the Weyl tensor and fluid velocity properties.

Findings

Perfect-fluid space-time with irrotational velocity vector is a generalized Robertson-Walker space-time.

Null divergence of the Weyl tensor characterizes these space-times.

Relation between pressure and energy density confirms the conditions.

Abstract

A perfect-fluid space-time of dimension n>3 with 1) irrotational velocity vector field, 2) null divergence of the Weyl tensor, is a generalised Robertson-Walker space-time with Einstein fiber. Condition 1) is verified whenever pressure and energy density are related by an equation of state. The contraction of the Weyl tensor with the velocity vector field is zero. Conversely, a generalized Robertson-Walker space-time with null divergence of the Weyl tensor is a perfect-fluid space-time.