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

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 Einstein–Maxwell spacetimes. It is shown that although the expression based on the anti-holomorphic spinors is finite and unambiguously defined only in the centre-of-mass frame (i.e. it diverges in general), the corresponding Pauli–Lubanski spin is always finite, free of gauge 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 the presence of outgoing gravitational radiation. For stationary spacetimes both constructions reduce to the ‘standard’ expression.