On Static Solutions of Einstein's Generalized Theory of Gravitation, I

In Einstein's generalized theory of gravitation, we clarify the expressions of the basic quantity of the electromagnetic field and define "field strength" so as to introduce "four-vector potential ". When the distribution of matter and charge is static and spherically symmetric, we can choose, by using the electrostatic potential, a suitable boundary condition independently of the coordinate system used and can overcome the difficulty of Wyman and others. After that the asymptotic behaviour of Wyman's solution is studied and the resulting forms are found to be satisfactory. The mutual effect of matter and charge is also discussed and the results are compared with those of general relativity for a point charge.