Rainich geometrization is the process of eliminating the source from Einstein's field equations and thus expressing the equations solely with geometric quantities. This report briefly covers the theory, due to Kuchar, involved in the Rainich geometrization of a real massless scalar field with no cosmological constant. The theory contains the conditions which the Ricci tensor must satisfy such that the spacetime permits the scalar field and also explains the method used to reconstruct the field. Two procedures are written which automate this process and they are used extensively through the rest of the paper to both verify existing solutions, such as Fisher's (alternatively, the JNW solution) and Xanthopoulos', and to compute other solutions from generic spacetimes.
Krongos, Dionisios, "Rainich Geometrization of Real Massless Scalar Fields" (2014). Physics Capstone Projects. Paper 12.