Scalar-tensor propagation of light in the inner solar system at the millimetric level

TL;DR

This paper extends the metric equations in General Relativity to include scalar-tensor theories, providing explicit solutions for light propagation in the inner solar system at millimetric precision, relevant for upcoming space experiments.

Contribution

It introduces an extension of the IAU metric equations to scalar-tensor theories and derives explicit geodesic solutions for light propagation at millimetric accuracy in the solar system.

Findings

Extended metric equations to scalar-tensor theories.

Derived explicit geodesic solutions for light propagation.

Applicable to high-precision space experiments.

Abstract

In a recent paper [1], motivated by forthcoming space experiments involving propagation of light in the Solar System, we have proposed an extention of the IAU metric equations at the c-4 level in General Relativity. However, scalar-tensor theories may induce corrections numerically comparable to the c-4 general relativistic terms. Accordingly, one first proposes in this paper an extension of [1] to the scalar-tensor case. The case of a hierarchized system (such as the Solar system) is emphasized. In this case, the relevant metric solution is proposed. Then, the geodesic solution relevant for propagation of light in the inner solar system at the millimetric level is given in explicit form.