Sheer-free perfect fluids in general relativity: Gravito-magnetic spacetimes

We investigate shear-free, perfect fluid solutions of Einstein's field equa tions in which the perfect fluid satisfies a barotropic equation of state p = p(w) such that w + p not equal 0. We find that if the electric part of t he Weyl tensor (with respect to the fluid how) vanishes and the spacetime i s not conformally flat then the fluid volume expansion is zero but the vort icity is necessarily nonzero. In addition, we show that if p = -w/3 then ne cessarily either the fluid expansion is zero or the fluid vorticity is zero .