Very recently, a straightforward way was proposed in order to understand the galaxy and
galactic cluster world without using the very elusive dark matter concept. This way was called
κ-model [1, 2, 3, 4]. The main idea is to save the form of the usual physical laws, especially the
Newton’s laws of motion when gravity is weak, but only by applying a local renormalization
procedure for the lengths, distances and velocities. This local renormalization appears as a
correspondance principle in the κ-model. In this model the fundamental physical constants
remain universal, i.e. are independent of the point and of time. The κ-model is Newtonian
in essence but a relativistic extension can easily be built. The aim of the present paper is to
detail the mathematical formalism supporting i