On quasi-local angular momentum and the construction of axial vector fields

A method is introduced which, for the first time, allows us to construct axial vector fields without which formal definitions of quasi-local angular momentum, in general, would remain empty. The introduced method is practical, it can be used to construct all such axial vector fields, and it allows the quasi-local angular momentum to be represented by a triple vector in three-dimensional Euclidean space. We also derive balance relations which allow us to monitor the variation of the magnitude and direction of this vector, and also to monitor the angular momentum transports in generic spacetimes without symmetries.