Abstrakt
We study the self-force acting on a static charged pointlike particle near a Schwarzschild black hole. We obtain the pointlike particle as a limit of a spacetime describing a big neutral black hole with a small charged massive object nearby.
The massive object is modeled by a black hole or a naked singularity. In this fully interacting system the massive object is supported above the black hole by a strut.
Such a strut has a nonzero tension which corresponds to the external force compensating the gravitational force and the electromagnetic self-force acting on the massive object. We discuss details of the limiting procedure leading to the pointlike particle situation.
As a result, we obtain the standard gravitational force in the static frame of the Schwarzschild spacetime and the electromagnetic self-force. The electromagnetic self-force differs slightly from the classical results in a domain near the horizon.
The difference is due to taking into account the influence of the strut on the electromagnetic field. We also demonstrate that higher order corrections to the gravitational force, a sort of gravitational self-force, are not uniquely defined, and they depend on details of the limiting procedure.