Periapsis shift in spherically symmetric spacetimes and effect of electric interaction

The periapsis shift of charged test particles in arbitrary static and spherically symmetric charged spacetimes are studied. Two perturbative methods, the near-circular approximation and post-Newtonian methods, are developed, and shown to be very accurate when the results are found to high orders. The former method is more precise when the eccentricity $e$ of the orbit is small while the latter works better when the orbit semilatus rectum $p$ is large. Results from these two methods are shown to agree with each other when both $e$ is small and $p$ is large. These results are then applied to the Reissner-Nordstr\"om spacetime, the Einstein-Maxwell-dilation gravity and a charged wormhole spacetime. The effects of various parameters on the periapsis shift, especially that of the electrostatic interaction, are carefully studied. The periapsis shift data of the solar-Mercury is then used to constrain the charges of the Sun and Mercury, and the data of the Sgr A$^*$-S2 periapsis shift is used to find, for the first time using this method, constraints about the charges of Sgr A$^*$ and S2.
Comment: 17 pages, 9 figures