Key points are not available for this paper at this time.
The Einstein equations of the general theory of relativity are solved for an energy-momentum tensor derived from a linear scalar field theory specialized to a static spherically symmetric field of a point-like source. This is the scalar analog to the structure of the field about a point electron. However, the mathematics is more complicated. A two-parameter family of line elements and associated fields is discovered, of which the Schwarzschild solutions from a one-parameter subfamily. The g₈₊ and field variable V can be only implicitly expressed as algebraic and logarithmic functions of r, except for special one-parameter subfamilies where explicit expressions are obtainable. However, asymptotic approximations for large and small radius are derived except for one of the one-parameter subfamilies.
Bergmann et al. (Thu,) studied this question.