On the calculation of the geodetic distance and associated invariants in relativistic gravitational fields

In the static spherically symmetric case, the calculation of the world function of Riemannian space-time, i.e., essentially, the square of the geodetic distance of two events, which is determined by a system of nonlinear differential equations, is reduced to quadrature and elimination problems. Then the symmetry-adapted construction of further invariants of space-time built up by derivatives of the world function is given. By applying the derived basic scheme to special families of model metrics, which are interpreted as Einstein gravitational potentials, explicit exact results for the considered two-point scalars are obtained. (author)