Adiabatic theory of motion of bodies in the Hartle-Thorne spacetime

TL;DR

This paper develops an adiabatic theoretical framework using the Hartle-Thorne metric to analyze test particle motion in the gravitational field of rotating, deformed bodies, successfully deriving perihelion shift formulas consistent with observations.

Contribution

It introduces a novel application of adiabatic theory with the Hartle-Thorne metric to derive perihelion shifts, confirming the superposition principle for gravitational effects.

Findings

Perihelion shift formula derived for equatorial orbits.

Results agree with observational data for Solar system planets.

Corrections from Sun's angular momentum and quadrupole moment are minimal.

Abstract

We study the motion of test particles in the gravitational field of a rotating and deformed object within the framework of the adiabatic theory. For this purpose, the Hartle-Thorne metric written in harmonic coordinates is employed in the post-Newtonian approximation where the adiabatic theory is valid. As a result, we obtain the perihelion shift formula for test particles orbiting on the equatorial plane of a rotating and deformed object. Based on the perihelion shift expression, we show that the principle of superposition is valid for the individual effects of the gravitational source mass, angular momentum and quadrupole moment. The resulting formula was applied to the inner planets of the Solar system. The outcomes are in a good agreement with observational data. It was also shown that the corrections related to the Sun's angular moment and quadrupole moment have little impact on the perihelion shift. On the whole, it was demonstrated that the adiabatic theory, along with its simplicity, leads to correct results, which in the limiting cases correspond to the ones reported in the literature.