Abstract
The Ludvigsen-Vickers and two recently suggested quasi-local spin-angular momentum expressions, based on holomorphic and anti-holomorphic spinor fields, are calculated for small spheres of radius r about a point o. It is shown that, apart from the sign in the case of anti-holomorphic spinors in non-vacuum, the leading terms of all these expressions coincide. In non-vacuum spacetimes this common leading term is of order r4, and it is the product of the contraction of the energy-momentum tensor and an average of the approximate boost-rotation Killing vector that vanishes at o and of the 3-volume of the ball of radius r. In vacuum spacetimes the leading term is of order r6, and the factor of proportionality is the contraction of the Bel-Robinson tensor and another average of the same approximate boost-rotation Killing vector.
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