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In this article, the question of the nature of cold dark matter is approachedfrom a new angle. By invoking the Cauchy problem of relativity it is shown how,under very precise astrophysical conditions, the Einstein general theory ofrelativity is formally equivalent to the Ginzburg-Landau theory ofsuperconductivity. This fact lead us to suspect that the superconductivity ofgravitation ought to be a real physical process occurring in the outskirts ofgalaxies. It is found that quantum mechanically gravity can achieve a type-IIsuperconductor state characterised by the Gizburg-Landau parameter$\kappa=1.5$, and it is suggested that a probability flux of Cooper pairs(quantum gravitational geons charged with vacuum energy) are directlyresponsible for the flatness exhibited by the rotation curves in spiralgalaxies, as well as the exotic behaviour observed in galactic clustercollisions. If this hypothesis proves correct, the whole phenomenon of darkmatter may count, after all, as another triumph for Einstein's theory ofgravity. The tension between gravitation and quantum mechanics is exploredfurther by a subtle consideration of the Hamilton-Jacobi theory of theYork-time action, providing additional motivation for the above line ofreasoning. In particular, Penrose's estimate for the rate of collapse of thewavefunction is recovered, and connected to the instability of Misner space.

Theory of superconductivity of gravitation and the dark matter enigma