On the combined Dirac–Einstein–Maxwell field equations

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Abstract
This paper discusses the combined Dirac–Einstein–Maxwell equations in general relativity. The combined equations are derived from a variational principle which involves the variation of tetrad fields. A class of exact, self‐consistent solutions is found where the metric is static, the electromagnetic field is just electrostatic, and the spinor field is stationary in the wave mechanical sense. These solutions are analogous to Dirac’s plane wave solutions which propagate along the x3 axis and are not square integrable. It is shown that under reasonable physical conditions there do not exist solutions with finite total charge. It seems that the static electro‐gravitational background is not compatible with localizable matter fields possessing intrinsic spin.

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