Isometries compatible with asymptotic flatness at null infinity: A complete description

The following results concerning isometrics of space-times which are asymptotically empty and flat at null infinity are established: (i) The isometry group is necessarily a subgroup of the Poincaré group; (ii) if the asymptotic Weyl curvature is nonzero - more precisely, in the standard notation, if K_abcdn^d does not vanish identically on ℐ - the space-time cannot admit more than two Killing fields unless the metric is Schwarzschildean in a neighborhood ℐ, if it does admit two Killing fields, they necessarily commute; one (and only one) of them is a translation; the radiation field as well as the Bondi news vanishes everywhere on ℐ; and, finally, if the translational Killing field is timelike in a neighborhood of ℐ, the other Killing field is necessarily rotational. Several implications of these results are pointed out.