Perfect fluid space-times whose energy-momentum tensor is conformal Killing

Abstract

We show that the energy-momentum tensor T of an expanding perfect fluid space-time (M,g) is a nontrivial conformal Killing tensor if and only if M is shear-free, vorticity-free, and satisfies certain energy and force equations. In particular, if T is conformal Killing, we show that the perfect fluid is stationary and its energy-density and pressure are constant.