Projective and Carrollian geometry at time/space-like infinity on projectively compact Ricci flat Einstein manifolds

In this article we discuss how to construct canonical strong Carrollian geometries at time/space like infinity of projectively compact Ricci flat Einstein manifolds (M, g) and discuss the links between the underlying projective structure of the metric g. The obtained Carrollian geometries are determined by the data of the projective compactification. The key idea to achieve this is to consider a new type of Cartan geometry based on a non-effective homogeneous model for projective geometry. We prove that this structure is a general feature of projectively compact Ricci flat Einstein manifolds.