Null-infinity, here taken to mean the conformal boundary of an asymptotically-flat space-time, is strictly speaking not a conformal manifolds, rather the induced conformal metric is degenerate with null direction spanned by a prefered (weighted) vector field. It is well-known that automorphisms of such structure correspond to the BMS group and it is rather natural to wonder if one can developp a systematic tractor approach adapted to such degenerate conformal geometries. We will show that this can be achieved and that it neatly relates to the physics of asymptotically-flat space-times.
The main new feature, as opposed to the usual situtation, is that the normal tractor connection is NOT unique for such degenerate geometries (this is closely similar to 2D conformal geomtries). Rather there is an infinite-dimensional family of normal connections and one can show that this freedom is related to the freedom in gravitational radiations reaching null-infinity.
More precisely, the freedom in normal connection at null-infinity invariantly encode the freedom in asymptotic shears of would be null-geodesic congruences for the corresponding asymptotically-flat space-time. It follows that curvature of the tractor connection then is the obstruction to the existence of an asymptotically shear-free congruence and therefore intrisically characterise presence of gravitational radiations.
We will also discuss relation to ambient tractors and with Penrose' asymptotic twistors.