In the weak field approximation to the gravitational field equations, we study gravitational paramagnetism and diamagnetism, the gravitational Meissner effect and gravitational superconductivity.The spontaneous symmetry breaking corresponds to crossing from closed geodesics to open ones, and to the existence of a critical temperature in the frame of a gauge model at finite temperature. In this later case one can obtain expressions giving the dependence of several superconducting parameters on temperature.

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Identifying space with a superconducting cosmic dust, the structure of the ‘world crystal’ is built. Particles moving on open geodesics are assimilated with the ‘electron gas’ in a lattice, and those moving on closed geodesics with nodes of the same lattice. By considering that this kind of structure may be achieved by pinning on a background gravitomagnetic field, the properties of such fields are studied. From this analysis and computing the background energy we are lead to a Cantorian-fractal structure of space–time, which allows one to interpret the gravitational interaction in terms of a mechanism similar to the composite fermions mechanism.

It is shown that in terms of the fractal space–time theory the gravitoelectric potential is responsible for the quantisation of the planetary and binary galaxy motions. On a cosmic scale a homogeneous gravitomagnetic field allows not only an ordering of the Universe, but a ‘global’ redshift quantisation of galaxies as well.