# Post-Keplerian motion in Reissner-Nordstr\"{o}m spacetime

## TL;DR

This paper derives analytical post-Newtonian solutions for test particle motion in Reissner-Nordström spacetime across multiple representations, linking parameters to energy and angular momentum.

## Contribution

It provides the first comprehensive formulation of post-Newtonian solutions in Reissner-Nordström spacetime in various representations, connecting parameters to physical quantities.

## Key findings

- Analytical post-Newtonian solutions in four representations.
- Relations established between (post-)Keplerian parameters and physical quantities.
- Framework enables better understanding of charged black hole orbits.

## Abstract

We present the analytical post-Newtonian solutions for the test particle's motion in the Reissner-Nordstr\"{o}m spacetime. The solutions are formulated in the Wagoner-Will representation, the Epstein-Haugan representation, the Brumberg representation, and the Damour-Deruelle representation, respectively. The relations between the (post-)Keplerian parameters in different representations, as well as their relations to the orbital energy and angular momentum are also provided.