Post-linear metric of a solar system body

TL;DR

This paper discusses the development of a post-linear metric tensor model for solar system bodies using the Multipolar Post-Minkowskian formalism to achieve ultra-precise light trajectory calculations.

Contribution

It introduces a method to derive the metric tensor of solar system bodies in post-linear approximation using the Multipolar Post-Minkowskian formalism.

Findings

Framework for determining metric density around solar bodies

Method to derive the metric tensor from field equations

Enhanced accuracy for light trajectory modeling

Abstract

A precise modeling of light trajectories in the solar system on the sub-micro-arcsecond and nano-arcsecond scale of accuracy requires the metric tensor of solar system bodies in post-linear approximation. The Multipolar Post-Minkowskian formalism represents a framework for determining the metric density in the exterior of a compact source of matter, which can be regarded as massive solar system body. The knowledge of the metric density, frequently been called gothic metric, allows to deduce the metric tensor. Some aspects are considered about how to determine the metric density and the metric tensor from the field equations of gravity.