Light propagation in 2PN approximation in the field of one moving monopole: I. Initial value problem

TL;DR

This paper analyzes light propagation in a gravitational field of a moving monopole using second post-Newtonian approximation, highlighting the impact of the body's acceleration on light trajectory and providing formulas for light deflection and time delay.

Contribution

It introduces a detailed second post-Newtonian model for light propagation in the field of a moving monopole, including acceleration effects.

Findings

Acceleration of the body affects light trajectory.

Certain acceleration terms are essential for well-defined logarithmic functions.

Negligible acceleration terms do not impact pico-second level measurements.

Abstract

In this investigation the light propagation in the gravitational field of one arbitrarily moving body with monopole structure is considered in the second post-Newtonian approximation. It is found that the light trajectory depends on the acceleration of the body. Some of these acceleration terms are important in order to get well-defined logarithmic functions with dimensionless arguments, while all the other acceleration terms are negligible on the pico-second level of accuracy in time-delay measurements. The expressions of the observables total light deflection and time delay are determined.