Asymptotically flat spacetimes form a class of solutions to Einstein's equations which model isolated systems in General Relativity. In particular, gravitational radiations leaking away from these spacetimes are encoded by geometrical data "at infinity". These facts are technically well understood and form the conceptual bedrock for gravitational waves prediction. Despite this, many results typically appear as technical and seemingly coordinate dependent. However, as I will explain, conceptual clarity can be obtained through the use of Cartan geometry methods and Tractor geometry. From this perspective, gravitational characteristic data at null-infinity invariantly correspond to a choice of 3-dimensional Cartan geometry while the presence of radiation corresponds to curvature. The situation is in fact very similar to two dimensional conformal geometry where conformal Cartan geometries are not uniquely associated to a conformal geometry (Möbius structure need to be introduced) and one can draw an enlightening parallel, with holomorphic transformations playing the role of the BMS group. This also gives a precise geometrical meaning to the typical statement that "gravitational radiation is the obstruction to having a distinguished Poincaré group as asymptotic symmetries".
Meeting ID: 898 5941 9685