Algebraically special coplanar shear-free perfect fluids in general relativity

We investigate all algebraically special, not conformally flat, shear-free, isentropic (<i>p</i>(<i>w</i>), <i>w</i> + <i>p</i> ≠ 0), perfect fluid solutions of Einstein's field equations. We show, using the GHP formalism, that if the repeated principle null direction of the Weyl tensor is coplanar with the fluid's 4-velocity and vorticity vector (assumed nonzero), then the fluid's expansion must vanish.<br />