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