Space-Time Structure of a Static Spherically Symmetric Scalar Field

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 ${g}_{\mathrm{ik}}$ 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.

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