Tractor geometry of asymptotically flat spacetimes

Abstract

In a recent work it was shown that conformal Carroll geometries are canonically equipped with a null-tractor bundle generalizing the tractor bundle of conformal geometry. We here show that in the case of the conformal boundary of an asymptotically flat spacetime of any dimension d>=3, this null-tractor bundle over null infinity can be canonically derived from the interior spacetime geometry. As was previously discussed, compatible normal connections on the null-tractor bundle are not unique: We prove that they are in fact in one-to-one correspondence with the germ of the asymptotically flat spacetimes to leading order. In dimension d=3 the tractor connection invariantly encodes a choice of mass and angular momentum aspect, in dimension d>=4 a choice of asymptotic shear. In dimension d=4 the presence of tractor curvature correspond to gravitational radiation. Even thought these results are by construction geometrical and coordinate invariant, we give explicit expressions in BMS coordinates for concreteness.

This match the version published in Annales Henri Poincaré (2022)

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• Graviton scattering in self-dual radiative space-times
• Renormalization of conformal infinity as a stretched horizon
• Covariant canonical formulations of classical field theories
• Higher fundamental forms of the conformal boundary of asymptotically de Sitter spacetimes
• Asymptotic symmetries of projectively compact order one Einstein manifolds
• The gauging procedure and carrollian gravity
• Ti and Spi, Carrollian extended boundaries at timelike and spatial infinity