Shear-free perfect fluids with a $$\gamma $$ γ -law equation of state

Abstract

We investigate all shear-free perfect fluid solutions of the Einstein field equations where the pressure and energy density satisfy a \(\gamma \)-law equation of state with \(\mu +p\ne 0\). We prove that such a fluid is either non rotating or non expanding. As a consequence, it follows by combining our result with those of Collins and Wainwright that any such shear-free perfect fluid which models either an expand universe or a collapsing star must in fact be a Friedmann–Robertson–Walker spacetime.