### 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 [346]. 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 [346] that the Ludvigsen–Vickers spin angular momentum tends to that of Bramson at
future null infinity. For small spheres [494] in nonvacuum it reproduces precisely the expected result (4.10),
and in vacuum it is

We stress that in both the vacuum and nonvacuum 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.