Probing global aspects of a geometry by the self-force on a charge: Spherical thin-shell wormholes

Abstract

The self-interaction for a static point charge in the space-time of a thin-shell wormhole constructed connecting two identical Schwarzschild geometries is calculated in a series expansion. The electrostatic self-force is evaluated numerically. It is found to be attractive towards the throat except for some values of the throat radius proximate to the value of the Schwarzschild horizon, for which the force is repulsive or attractive depending on the position of the charge. The result differs from the self-force in the space-time of the Schwarzschild black hole, where it is always repulsive from the center. Although these wormhole and black hole geometries are locally indistinguishable, the different topologies of both backgrounds are manifested in the electrostatic field of a point charge.