Periapsis precession in general stationary and axisymmetric spacetimes

TL;DR

This paper develops two perturbative methods to analyze periapsis precession in stationary, axisymmetric spacetimes, applying them to various solutions including Kerr-Newman and Kerr-Sen, and constraining effects using astronomical data.

Contribution

It introduces two systematic perturbative approaches for periapsis shift calculations applicable to general orbits in stationary, axisymmetric spacetimes, and applies them to several exact solutions.

Findings

Periapsis shift formulas for Kerr-Newman, Kerr-Sen, and Kerr-Taub-NUT spacetimes.

Electric and NUT charges influence periapsis precession with opposite signs.

Constraints on charge effects from Mercury, satellite, and S2 star data.

Abstract

This work studies the periapsis shift in the equatorial plane of arbitrary stationary and axisymmetric spacetimes. Two perturbative methods are systematically developed. The first work for small eccentricity but very general orbit size and the second, which is post-Newtonian and includes two variants, is more accurate for orbits of large size but allows general eccentricity. Results from these methods are shown to be equivalent under small eccentricity and large size limits. The periapsis shift of Kerr-Newman, Kerr-Sen and Kerr-Taub-NUT spacetimes are computed to high orders. The electric charge and NUT charge are shown to contribute to the leading order but with opposite signs. The frame-dragging term and high-order effect of spacetime spin are given. The electric and NUT changes of the Earth, Sun and Sgr A* are constrained using the Mercury, satellite and S2 precession data. Periapsis shifts of other spacetimes are obtained too.