Tractor Geometry of Asymptotically Flat Spacetimes

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-tr...

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Veröffentlicht in:Annales Henri Poincaré 2022-09, Vol.23 (9), p.3265-3310
1. Verfasser: Herfray, Yannick
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description 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.
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subjects Angular momentum
Asymptotic properties
Classical and Quantum Gravitation
Dynamical Systems and Ergodic Theory
Elementary Particles
Geometry
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical Physics
Mathematics
Physics
Physics and Astronomy
Quantum Field Theory
Quantum Physics
Relativity
Relativity Theory
Spacetime
Theoretical
Tractors
title Tractor Geometry of Asymptotically Flat Spacetimes
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