Parametrized post-Newtonian equations of motion of N mass monopoles with the SEP violation

TL;DR

This paper derives parametrized post-Newtonian equations of motion for N mass monopoles allowing for potential violations of the Strong Equivalence Principle, enabling tests of gravity theories in solar system experiments.

Contribution

It provides a new derivation of PPN equations of motion for multiple monopoles including SEP violation, with explicit integrals and special cases for experimental testing.

Findings

Derived equations incorporate SEP violation parameters.

Provided classical integrals of motion for the system.

Discussed special cases with exact integrals.

Abstract

Post-Newtonian equations of motion of a system of $N$ mass monopoles in the framework of the PPN formalism with two parameters $\beta$ and $\gamma$ are derived for the case when the Strong Equivalence Principle can be violated. The derivation is based on the previously published general framework. The multipole moments of each body are defined as a PPN-generalization of the corresponding Blanchet-Damour multiple moments in a relevant local reference system defined for that body. The classical ten integrals of the derived equations of motion are given. A special version of the equations of motion, for which seven of these integrals are exact, is discussed. The derived equations of motion can be used to test the Strong Equivalence Principle in various solar system experiments.