Abstract

The magnetic dipole moment of the Kerr–Newman metric, defined by mass \, electrical charge \ and angular momentum \, is \, corresponding, for all values of \, to a gyromagnetic ratio \, which is also the value of the intrinsic gyromagnetic ratio of the electron, as first noted by Carter. Here, we argue that this result can be understood in terms of the particle-wave complementarity principle. For \ can only be defined at asymptotic spatial infinity, where the metric appears to describe a spinning point particle, and therefore setting \, \, we necessarily have a model of the electron. From the Dirac equation we can construct a covariantly conserved four-current \ that is the source of the electromagnetic field generated by the charge \. The result \ then follows from the minimal gauge principle \ which is implicit in the formulation of the spinorial wave equation, and which can also be justified from the line action for a spin-1/2 point particle interacting with an external electromagnetic field, due to Berezin and Marinov. By contrast, analysis of the gyrogravito-magnetic effect, investigated classically by Wald and quantum mechanically by Adler et al., yields the result \ in all non-relativistic cases, which can be explained from the principle of equivalence. The results are in accord with the correspondence principle