  Without observational or theoretical modifications, Newtonian and general
relativity seem to be unable to explain gravitational behavior of large
structure of the universe. The assumption of dark matter solves this problem
without modifying theories. But it implies that most of the matter in the
universe must be unobserved matter. Another solution is to modify gravitation
laws. In this article, we study a third way that doesn't modify gravitation
neither matter's distribution, by using a new physical assumption on the
clusters. Compare with Newtonian gravitation, general relativity (in its
linearized approximation) leads to add a new component without changing the
gravity field. As already known, this component for galaxies is too small to
explain dark matter. But we will see that the galaxies' clusters can generate a
significant component and embed large structure of universe. We show that the
magnitude of this embedding component is small enough to be in agreement with
current experimental results, undetectable at our scale, but detectable at the
scale of the galaxies and explain dark matter, in particular the rotation speed
of galaxies, the rotation speed of dwarf satellite galaxies, the expected
quantity of dark matter inside galaxies and the expected experimental values of
parameters $\Omega$\_dm of dark matter measured in CMB. This solution implies
testable consequences that differentiate it from other theories: decreasing
dark matter with the distance to the cluster's center, large quantity of dark
matter for galaxies close to the cluster's center, isolation of galaxies
without dark matter, movement of dwarf satellite galaxies in planes close to
the supergalactic plane, close orientations of spin's vectors of two close
clusters, orientation of nearly all the spin's vector of galaxies of a same
cluster in a same half-space, existence of very rare galaxies with two portions
of their disk that rotate in opposite directions...
