  A shear-free ray congruence on Minkowski space is a 3-parameter family of
null geodesics along which Lie transport of a complementary 2-dimensional
spacelike subspace (called the screen space) is conformal. Such congruences are
defined by complex analytic surfaces in the associated twistor space $\CP^3$
and are the basis of the construction of massless fields. On a more general
space-time, it is unclear how to couple the massless field with the
gravitational field. In this article we do this by considering the following
Cauchy-type problem: given a Riemannian 3-manifold $(M^3, g_0)$ endowed with a
unit vector field $U_0$ that is tangent to a conformal foliation, we require
that the pair extend to a space-time $({\mathcal M}, {\mathcal G})$ endowed
with a spacelike unit vector field $U_t$ in such a way that $U_t$
simultaneously generates null geodesics and is tangent to a conformal foliation
on spacelike slices $t=$ const.
