Radiative gravitational fields and asymptotically static or stationary initial data

We describe our present understanding of the relation between the behaviour near space-like infinity of asymptotically flat Cauchy data for Einstein’s vacuum field equations and the asymptotic behaviour of their time evolution at null infinity. It is shown that asymptotically flat, static vacuum solutions admit an analytic conformal representation in a neighbourhood of the critical sets at which null infinity touches the cylinder at space-like infinity.