The Reciprocal of the Fundamental Theorem of Riemannian Geometry

The fundamental theorem of Riemannian geometry is inverted for analytic Christoffel symbols. The inversion formula, henceforth dubbed Ricardo’s formula, is obtained without ancillary assumptions. Even though Ricardo’s formula can mathematically give the full answer, it is argued that the solution should be taken only up to a constant conformal factor. A procedure to obtain the Christoffel symbols out of unparameterized geodesics is sketched. Thus, a complete framework to obtain the metric out of measurements is presented. The framework is suitable for analysis of experiments testing the geometrical nature of gravity.