Post-Newtonian metric of general relativity including all the c-4 terms in the continuity of the IAU2000 resolutions

The Solar System metric recommended by the International Astronomical Union (IAU) resolution B1.3, during its 24th general assembly, allows light propagation calculations until order c-3 only. However, an increasing number of forthcoming spatial experiments will require a modelization of the gravitational field including all the c-4 terms in the metric to describe light propagation at the required precision. This will be the case for missions planned or in project, like TIPO, ASTROD, LATOR. Hence, it is necessary to extend the IAU framework to include all the relevant contributing terms. This paper proposes such an extension.