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

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Abstract
The following results concerning isometries 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 Kabcdnd does not vanish identically on I—the space–time cannot admit more than two Killing fields unless the metric is Schwarzschildean in a neighborhood of 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.
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