Total angular momentum from Dirac eigenspinors

TL;DR

This paper develops a gauge-invariant method to define angular momentum at null infinity using Dirac eigenspinors, connecting quantum spinor methods with gravitational angular momentum in general relativity.

Contribution

It introduces a novel approach to defining angular momentum at null infinity via eigenspinors of Dirac operators, linking quantum spinor techniques with gravitational physics.

Findings

Constructed divergence-free vector fields from eigenspinors that reproduce rotation symmetries.

Provided a gauge-invariant definition of spatial angular momentum at null infinity.

Derived a formula for angular momentum flux due to gravitational radiation.

Abstract

The eigenvalue problem for Dirac operators, constructed from two connections on the spinor bundle over closed spacelike 2-surfaces, is investigated. A class of divergence free vector fields, built from the eigenspinors, are found, which, for the lowest eigenvalue, reproduce the rotation Killing vectors of metric spheres, and provide rotation BMS vector fields at future null infinity. This makes it possible to introduce a well defined, gauge invariant spatial angular momentum at null infinity, which reduces to the standard expression in stationary spacetimes. The general formula for the angular momentum flux carried away be the gravitational radiation is also derived.