  The Multipolar Post-Minkowskian (MPM) formalism represents an approach for
determining the metric density in the exterior of a compact source of matter.
In the MPM formalism the metric density is given in harmonic coordinates and in
terms of symmetric tracefree (STF) multipoles. In this investigation, the
post-linear metric density of this formalism is used in order to determine the
post-linear metric tensor in the exterior of a compact source of matter. The
metric tensor is given in harmonic coordinates and in terms of STF multipoles.
The post-linear metric coefficients are associated with an integration
procedure. The integration of these post-linear metric coefficients is
performed explicitly for the case of a stationary source, where the first
multipoles (monopole and quadrupole) of the source are taken into account.
These studies are a requirement for further investigations in the theory of
light propagation aiming at highly precise astrometric measurements in the
solar system, where the post-linear coefficients of the metric tensor of solar
system bodies become relevant.
