A proposal for the missing mass : it is just the outer , far one

We reconsider the original argument, based on the virial theorem, by which Zwicky was first led to conjecture the existence of a missing mass, and point out that, without any justification, he neglects the contribution of the forces due to the matter lying outside the considered system, Now, it is true that the contribution of the outer mass to the virial vanishes if the gravitational field is taken in the Newto-nian approximation. However, according to general relativity in the weak field approximation, the gravitational potential has to be taken at the retarded time. This fact introduces into the force an additional term which, quite unexpectedly, turns out to act as a pressure. Its contribution to the external virial is estimated. With the simplest assumptions, an extremely good agreement with the observations is found for the Coma cluster considered by Zwicky. Furthermore, it is found that the contribution of the outer matter increases linearly with the linear dimension of the system. This seems to be in qualitative agreement with the fact that the mass defect is known to increase with the scale of the considered system, from galactic objects to superclus-ters of galaxies. Let us recall what the virial theorem is, comparing the case of Clausius to that of Zwicky (see [Zwicky (1933)] ans [Zwicky (1937)]). One considers 1