# Formal proof of some inequalities used in the analysis of the post-post-Newtonian light propagation theory - Astrophysics > Instrumentation and Methods for Astrophysics

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Abstract: A rigorous analytical solution of light propagation in Schwarzschild metricin post-post Newtonian approximation has been presented in \cite{report1}. In\cite{report2} it has been asserted that the sum of all those terms which areof order ${{\cal O} \frac{m^2}{d^2}}$ and ${{\calO}\frac{m^2}{d \sigma^2}}$ is not greater than $15-4 \pi \frac{m^2}{d^2}}$and $15-4 \pi \frac{m^2}{d \sigma^2}}$, respectively. All these terms can beneglected on microarcsecond level of accuracy, leading to considerablysimplified analytical transformations of light propagation. In this report, wegive formal mathematical proofs for the inequalities used in the appendices of\cite{report2}.

Autor: Sven Zschocke, Sergei A. Klioner

Fuente: https://arxiv.org/