From the real parts of one of the asymptotic Bianchi identities, Equation (56), we found the
standard kinematic expression for the Bondi linear momentum, with extra
terms and the Mathisson–Papapetrou spin coupling, among others. The imaginary
part was the angular momentum conservation law with a very natural looking flux expression
of the form:
+ FluxE&M Quad
+ FluxE&M dipole
J = spin + orbital + precession + varying magnetic dipole + quadrupole terms.
The last flux term is identical to that calculated from classical electromagnetic theory.