Asymptotic Gravitational Field of the ``Electron''

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Abstract
The Einstein‐Maxwell equations appropriate to the exterior metric and fields of a source characterized by mass, electric charge, and magnetic dipole moment are formulated. Because of the presence of a nonvanishing Poynting vector, the metric tensor must include off‐diagonal elements. A rigorous reduction of the metric tensor to three unknown functions is accomplished and the field equations are solved to second order in the gravitational constant. Using the parameters of the electron and proton, we find that the magnetic dipole terms dominate the metric at small distances and that general relativistic effects become important at distances of the order of 10−22 cm. Possible applications of the asymptotic metric are discussed.