Starting with some basic facts about the gyromagnetic factor g in Maxwell's theory, we review the special role played by a g factor g = 2 in quantum mechanics and elementary particle physics, and we draw attention to the same value g = 2 for the black holes and many other (electro-)vacuum solutions of general relativity. We strengthen and extend this special role of g = 2 in general relativity by considering a class of slowly rotating, charged mass shells, showing that the black-hole value g = 2 is extremely robust. Therefrom, we advance the hypothesis that the coincidence between these preferred g values signifies a deep common root of quantum theory and general relativity.
We calculate explicitly the system of a spherical shell of radius R, carrying ͑nearly͒ arbitrary mass M and charge q, and rotating slowly around an axis through its center. We discuss, mainly graphically in the plane of the model parameters M /R and q/R, the following properties of this system: The dragging of inertial frames which turns over to antidragging in part of the parameter space, the induced magnetic field, the angular momentum, the magnetic moment, and the gyromagnetic ratio. The latter is very near to the value 2 in an overwhelming part of the parameter space, and we argue that this signals a deep connection between general relativity and quantum theory which could be important in the search for quantum gravity.
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