From Kepler problem to skyrmions

Abstract

The classical treatment of the Kepler problem leaves room for the description of the space region of the central body by a hyperbolic geometry. If the correspondence between the empty space and the space filled with matter is taken to be a harmonic mapping, then the region of atomic nucleus, like the one of the Sun for the planetary system proper, is described by hyperbolic skyrmions. This fact makes possible the description of the nuclear matter within framework of general relativity. The classical “hedgehog” solution for skyrmions can then be classically interpreted in terms of the characterizations of intra-nuclear forces.