Theory of non-local point transformations - Part 2: General form and Gedanken experiment

The problem is posed of further extending the axiomatic construction proposed in Part 1 for non-local point transformations mapping in each other different curved space times. The new transformations apply to curved space times when expressed in arbitrary coordinate systems. It is shown that the solution permits to achieve an ideal (Gedanken) experiment realizing a suitable kind of phase-space transformation on point-particle classical dynamical systems. Applications of the theory are discussed both for diagonal and non-diagonal metric tensors.