On certain quasi-local spin-angular momentum expressions for large spheres near the null infinity

TL;DR

This paper evaluates quasi-local spin-angular momentum expressions near null infinity in asymptotically flat spacetimes, showing that certain formulations yield finite, unambiguous gravitational spin measures, especially in the center-of-mass frame.

Contribution

It demonstrates that the anti-holomorphic spinor-based expression provides a finite, unambiguous gravitational spin at null infinity, unlike the holomorphic version which diverges with radiation.

Findings

Anti-holomorphic spinor expression is finite in the center-of-mass frame.

Pauli-Lubanski spin derived from anti-holomorphic spinors is free of ambiguities.

Holomorphic spinor expression diverges with outgoing gravitational radiation.

Abstract

The recently suggested quasi-local spin-angular momentum expressions, based on the Bramson superpotential and on the holomorphic or anti-holomorphic spinor fields, are calculated for large spheres near the future null infinity of asymptotically flat Einsten-Maxwell spacetimes. It is shown that although the expression based on the anti-holomorphic spinors is finite and unambiguously defined only in the center-of-mass frame (i.e. it diverges in general), the corresponding Pauli-Lubanski spin is always finite, free of ambiguities, and is built only from the gravitational data. Thus it defines a gravitational spin expression at the future null infinity. The construction based on the holomorphic spinors diverges in presence of outgoing gravitational radiation. For stationary spacetimes both constructions reduce to the `standard' expression.