Post-linear metric of a solar system body

A precise modeling of light trajectories in the solar system on the sub-micro-arcsecond and nano-arcsecond scale of accuracy requires the metric tensor of solar system bodies in post-linear approximation. The Multipolar Post-Minkowskian formalism represents a framework for determining the metric density in the exterior of a compact source of matter, which can be regarded as massive solar system body. The knowledge of the metric density, frequently been called gothic metric, allows to deduce the metric tensor. Some aspects are considered about how to determine the metric density and the metric tensor from the field equations of gravity.