Uniqueness of the Friedmann-Lemaître-Robertson-Walker universes

We consider spacetimes with a perfect fluid distribution characterized by the energy density $\mu$, pressure $p$, charge density $\zeta$, and an equation of state $p=p\left(\mu \right)$, or $p\equiv 0$. It is shown that the only nonstatic isotropic solution of the Einstein-Maxwell equations where the contraction or expansion of the matter is shear free and the equation of state is physically reasonable is the Friedmann-Lemaître-Robertson-Walker class of solutions. Moreover, this conclusion holds for neutral matter even when the assumption of isotropy is replaced by the weaker hypothesis of irrotational motion.