Explicit form of the Scalar-Tensor metric to be used for propagation of light in the Solar system in continuity of the GR IAU2000 metric

Abstract: The metric recommanded by the IAU2000 resolutions allows propagation of light calculations at the c-3 level in the general relativity framework. In a paper [1], motivated by forthcoming space experiments involving propagation of light in the Solar System (ASTROD, GAIA, LATOR, ODYSSEY, SAGAS, SIM, TIPO, ...), we have proposed an extention of the IAU metric equations at the c-4 level. This has been made in the general relativity framework. However, scalar-tensor theories may induce corrections numerically comparable to the c-4 general relativistic terms. Accordingly, one proposes in this paper an extension of [1] to the scalar-tensor case. The case of a strongly hierarchized system (such as the Solar system) is emphasized. In this case, an explicit metric solution is proposed.