Carrollian manifolds and null infinity: A view from Cartan geometry

TL;DR

This paper explores the geometric structure of null infinity in general relativity using Cartan geometry, clarifying its relation to Carrollian geometries and the implications for gravitational radiation and asymptotic symmetries.

Contribution

It provides a unifying Cartan geometric framework for understanding null infinity and its associated Carrollian geometries, elucidating the geometric nature of gravitational radiation.

Findings

Null infinity can be viewed as a strongly Carrollian geometry.

Different Carrollian geometries are related through gauge choices.

Gravitational radiation obstructs the Poincaré group as asymptotic symmetries.

Abstract

We discuss three different (conformally) Carrollian geometries and their relation to null infinity from the unifying perspective of Cartan geometry. Null infinity \emph{per se} comes with numerous redundancies in its intrinsic geometry and the two other Carrollian geometries can be recovered by making successive choices of gauge. This clarifies the extent to which one can think of null infinity as being a (strongly) Carrollian geometry and we investigate the implications for the corresponding Cartan geometries. The perspective taken, which is that characteristic data for gravity at null infinity are equivalent to a Cartan geometry for the Poincar\'e group, gives a precise geometrical content to the fundamental fact that ``gravitational radiation is the obstruction to having the Poincar\'e group as asymptotic symmetries''.