  Using an integral definition to calculate the relativistic multipole moments
(RMM), and the ensuing generalized relativistic Gauss theorem, we prove that
the evaluation of that volume integral in Erez-Rosen coordinates, leads to a
specific link between the RMM and the source of the exterior space--time,
provided we have a global static axisymmetric metric in that coordinate system
for any Weyl exterior field. This result allows to establish a relationship
between the RMM and certain volume integral expressions involving the material
content of the source from its energy-momentum tensor as well as the interior
metric. In particular the relativistic quadrupole moment for the Erez-Rosen
space-time is obtained.
