Self-force on a static particle near a black hole

TL;DR

This paper investigates the electromagnetic self-force on a static charged particle near a Schwarzschild black hole, revealing subtle differences from classical results due to the influence of a supporting strut and the limiting process.

Contribution

It introduces a new limiting procedure to derive the self-force on a static particle near a black hole, accounting for the strut's influence and higher order correction ambiguities.

Findings

Electromagnetic self-force near the horizon differs slightly from classical predictions.

The limiting procedure affects the calculated gravitational self-force.

The strut's tension influences the electromagnetic field around the particle.

Abstract

We study the self-force acting on a static charged point-like particle near a Schwarzschild black hole. We obtain the point-like 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 non-zero 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 point-like 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 an influence of the strut on the electromagnetic field. We also demonstrate that higher order corrections to the gravitational force, a sort of the gravitational self-force, are not uniquely defined and they depend on details of the limiting procedure.