  In this article we propose a new geometrization of the radiative phase space
of asymptotically flat space-times: we show that the geometry induced on
null-infinity by the presence of gravitational waves can be understood to be a
generalisation of the tractor calculus of conformal manifolds adapted to the
case of degenerate conformal metrics. It follows that the whole formalism is,
by construction, manifestly conformally invariant. We first show that a choice
of asymptotic shear amounts to a choice of linear differential operator of
order two on the bundle of scales of null-infinity. We refer to these operators
as Poincar\'e operators. We then show that Poincar\'e operators are in
one-to-one correspondence with a particular class of tractor connections which
we call "null-normal" (they generalise the normal tractor connection of
conformal geometry). The tractor curvature encodes the presence of
gravitational waves and the non-uniqueness of flat null-normal tractor
connections correspond to the "degeneracy of gravity vacua" that has been
extensively discussed in the literature. This work thus brings back the
investigation of the radiative phase space of gravity to the study of (Cartan)
connections and associated bundles. This should allow, in particular, to
proliferate invariants of the phase space.
