In recent years there has been a resurgence of interest for asymptotic symmetries of gravity in relation to soft theorems, in particular there has been a renewed emphasis on the fact that "gravity vaccua" are not unique. In this talk I will discuss the underlying classical geometry responsible for this degeneracy of gravity vacua from the modern perspective of Cartan geometry. I will show that the conformal boundary of an asymptotically flat space-time is always equipped with a Cartan geometry (modelled on a realisation of flat null-infinity as an homogenous space for the 4D Poincaré group). The curvature of this induced geometry invariantly encodes the presence of gravitational radiations and the moduli of flat Cartan geometry corresponds to gravity vacua. Besides the conceptual clarity brought by these results I will also explain why they suggest possible generalisation to super-gravity and higher-spins that have never been considered.
