Quasi-local spin-angular momentum and the construction of axial vector fields

Abstract

A novel procedure is presented which allows the construction of all axial vector fields on Riemannian two-spheres. Using these axial vector fields and the centre-of-mass unit sphere reference systems, a constructive definition of quasi-local spin-angular momentum is introduced. Balance relations are also derived, with respect to arbitrary Lie-propagated unit sphere reference systems, to characterize the angular momentum transports in spacetimes without symmetries.