Inheriting geodesic flows

Abstract

We investigate the propagation equations for the expansion, vorticity and shear for per- fect fluid space-times which are geodesic. It is assumed that space-time admits a conformal Killing vector which is inheriting so that fluid flow lines are mapped conformally. Simple constraints on the electric and magnetic parts of the Weyl tensor are found for conformal symmetry. For homothetic vectors the vorticity and shear are free; they vanish for nonhomothetic vectors. We prove a conjecture for conformal symmetries in the special case of inheriting geodesic flows: there exist no proper con- formal Killing vectors ( ;ab =0) for perfect fluids except for Robertson–Walker space-times. For a nonhomothetic vector field the propagation of the quantityln(Rabuaub ) along the integral curves of the symmetry vector is homogeneous.