Light propagation in the 2PN approximation in the monopole and quadrupole field of a body at rest: Boundary value problem

TL;DR

This paper derives solutions for the boundary value problem of light propagation in the 2PN approximation considering monopole and quadrupole fields, crucial for high-precision tests of gravitational light deflection.

Contribution

It extends previous initial value problem solutions to boundary value problems in 2PN approximation for realistic finite-distance scenarios.

Findings

Derived boundary value solutions for light propagation in 2PN approximation.

Applicable to high-precision solar system gravitational tests.

Provides foundational results for future observational analyses.

Abstract

In a recent investigation, the initial value problem of light propagation in the gravitational field of a body at rest with monopole and quadrupole structure has been determined in the second post-Newtonian (2PN) approximation. In reality, the light source as well as the observer are located at finite distances from the solar system bodies. This fact requires solving the boundary value problem of light propagation. In this investigation, the solution of the boundary value problem is deduced from the initial value problem of light propagation in 2PN approximation. These results are a basic requirement for subsequent investigations aiming at ultra-highly precise tests of light deflection and time delay in the solar system.