  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.

General Relativity and Quantum Cosmology