Periapsis shift in spherically symmetric spacetimes and effects of electric interactions* *This work is partially Supported by the Wuhan University Research Development Fund

Abstract

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 determined to high orders. The near-circular approximation method is more precise when eccentricity e of the orbit is small, whereas the post-Newtonian method is more effective when orbit semilatus rectum p is large. Results from these two methods are shown to agree when both e is small and p is large. These results are then applied to the Reissner-Nordström spacetime, the Einstein-Maxwell-dilation gravity, and a charged wormhole spacetime. The effects of various parameters on the periapsis shift, particularly that of the electrostatic interaction, are carefully studied. The periapsis shift data of the solar-Mercury are then used to constrain the charges of the Sun and Mercury, and the data of the Sgr A*-S2 periapsis shift are used to determine, for the first time using this method, the constraints of the charges of Sgr A* and S2.