Angular momentum of isolated systems

TL;DR

This paper develops a twistorial approach to define angular momentum at null infinity in radiating space-times, ensuring meaningful comparisons across different cuts and revealing a unified view of shear and angular momentum.

Contribution

It introduces a BMS-invariant angular momentum definition using twistors, overcoming previous ambiguities and linking shear to higher-j contributions.

Findings

Angular momentum cannot be represented solely by a j=1 quantity.

Higher-j contributions to angular momentum correspond to shear.

The approach allows comparison of angular momentum across different cuts.

Abstract

Penrose's twistorial approach to the definition of angular momentum at null infinity is developed so that angular momenta at different cuts can be meaningfully compared. This is done by showing that the twistor spaces associated with different cuts of scri can be identified as manifolds (but not as vector spaces). The result is a well-defined, Bondi-Metzner-Sachs-invariant notion of angular momentum in a radiating space-time; the difficulties and ambiguities previously encountered are attached to attempts to express this in special-relativistic terms, and in particular to attempts to identify a single Minkowski space of origins. Unlike the special-relativistic case, the angular momentum cannot be represented by a purely j=1 quantity M_{ab}, but has higher-j contributions as well. Applying standard kinematic prescriptions, these higher-j contributions are shown to correspond precisely to the shear. Thus it appears that shear and angular momentum should be regarded as different aspects of a single unified concept.