### 9.1 The Ludvigsen-Vickers angular momentum

Under the conditions that ensured the Ludvigsen-Vickers construction for the energy-momentum would
work in Section 8.1, the definition of their angular momentum is straightforward [259]. Since in Minkowski
spacetime the Ludvigsen-Vickers spinors are just the restriction to of the constant spinor fields, by the
general remark above the Ludvigsen-Vickers spin-angular momentum is zero in Minkowski
spacetime.
Using the asymptotic solution of the Einstein-Maxwell equations in a Bondi-type coordinate system it
has been shown in [259] that the Ludvigsen-Vickers spin-angular momentum tends to that of Bramson at
future null infinity. For small spheres [360] in non-vacuum it reproduces precisely the expected result (29),
and in vacuum it is

We stress that in both the vacuum and non-vacuum cases the factor , interpreted in
Section 4.2.2 as an average of the boost-rotation Killing fields that vanish at , emerges
naturally. No (approximate) boost-rotation Killing field was put into the general formulae by
hand.