Carrollian and celestial spaces at infinity

Understand

We show that the geometry of the asymptotic infinities of Minkowski spacetime (in $d+1$ dimensions) is captured by homogeneous spaces of the Poincar\'e group: the blow-ups of spatial (Spi) and timelike (Ti) infinities in the sense of Ashtekar--Hansen and a novel space Ni fibering over $\mathscr{I}$.

• We embed these spaces \`a la Penrose--Rindler into a pseudo-euclidean space of signature $(d+1,2)$ as orbits of the same Poincar\'e subgroup of O$(d+1,2)$.
• We describe the corresponding Klein pairs and determine their Poincar\'e-invariant structures: a carrollian structure on Ti, a pseudo-carrollian structure on Spi and a "doubly-carrollian" structure on Ni.
• We give additional geometric characterisations of these spaces as grassmannians of affine hyperplanes in Minkowski spacetime: Spi is the (double cover of the) grassmannian of affine lorentzian hyperplanes; Ti is the grassmannian of affine spacelike hyperplanes and Ni fibers over the grassmannian of affine null planes, which is $\mathscr{I}$.