Light deflection in the second post-Newtonian approximation of scalar-tensor theory of gravity

TL;DR

This paper derives light deflection predictions in scalar-tensor gravity at the second post-Newtonian level, aiding high-precision astrometry missions that require ultra-accurate measurements of stellar positions.

Contribution

It provides a detailed derivation of light deflection in scalar-tensor gravity at 2nd post-Newtonian order, including intermediate range effects, for the first time.

Findings

Derived light deflection formulas at 2nd post-Newtonian order

Compared results with previous models, highlighting differences

Supported high-precision astrometry missions with improved theoretical framework

Abstract

In this paper, we use the metric coefficients and the equation of motion in the 2nd post-Newtonian approximation in scalar-tensor theory including intermediate range gravity to derive the deflection of light and compare it with previous works. These results will be useful for precision astrometry missions like GAIA (Global Astrometric Interferometer of Astrophysics), SIMS (The Space Interferometry Mission) and LATOR (Laser Astrometric Test Of Relativity) which aim at astrometry with microarcsecond and nanoarcsecond accuracies and need 2nd post-Newtonian framework and ephemeris to determine the stellar and spacecraft positions.