Cut-continuity of twistor angular momentum

TL;DR

This paper demonstrates that the twistor definition of angular momentum in Bondi-Sachs space-times varies continuously with the cut position at null infinity, responding to radiation correlations and offering a different perspective from existing definitions.

Contribution

It shows that the twistor angular momentum maintains cut-continuity and responds to radiation correlations, contrasting with other definitions that lack this property.

Findings

Twistor angular momentum is continuous with cut position.

The flux corresponds to the first variation of angular momentum.

It responds to correlations in radiation between asymptotic directions.

Abstract

Chen et al. argued recently that, in Bondi-Sachs space-times, the angular momentum at scri (null infinity) should vary continuously with the position of the cut (but not depend sensitively on its derivatives); they showed that this property was enjoyed by some definitions but not others. I show here that the twistor definition has this continuity. The argument is rather different from Chen et al.'s, with the invariant geometry of scri at the forefront. The flux, in the sense of the angular momentum emitted between two infinitesimally separated cuts, is calculated; this flux can be interpreted as the first variation of the angular momentum with respect to the cut. Examining the second variation, one finds that the twistor definition, unlike most others, responds to correlations in radiation between different asymptotic directions. The twistor angular momentum is thus sensitive to qualitatively different structure in the asymptotic field than are the currently more used ones.