  I show that radiative space-times are not asymptotically flat; rather, the
radiation field gives rise to holonomy at null infinity. (This was noted
earlier, by Bramson.) This means that, when gravitational radiation is present,
asymptotically covariantly constant vector fields do not exist. On the other
hand, according to the Bondi-Sachs construction, a weaker class of
asymptotically constant vectors does exist. Reconciling these concepts leads to
a measure of the scattering of matter by gravitational waves, that is, bulk
exchanges of energy-momentum between the waves and matter. Because these bulk
effects are potentially larger than the tidal ones which have usually been
studied, they may affect the waves' propagation more significantly, and the
question of matter's transparency to gravitational radiation should be
revisited. While in many cases there is reason to think the waves will be only
slightly affected, some situations are identified in which the energy-momentum
exchanges can be substantial enough that a closer investigation should be made.
In particular, the work here suggests that gravitational waves produced when
relativistic jets are formed might be substantially affected by passing through
an inhomogeneous medium.
